The free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].
What is oscillation sections?Oscillation sections are sections of a waveform that repeat themselves over a certain period of time. This period of time is known as the oscillation period and is typically measured in seconds or milliseconds.
The time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion can be found by summing the time intervals associated with the free-fall and oscillation sections of the motion.
The time interval associated with the 15.0 m free-fall can be found using the equation for the time it takes an object to fall a given distance, which is:
[tex]$t_{fall} = \sqrt{\frac{2d}{g}}$[/tex]
where d is the distance fallen and g is the acceleration due to gravity, which is [tex]9.81 m/s$^2$.[/tex]
Therefore, the time interval associated with the free-fall can be calculated as follows:
[tex]$t_{fall} = \sqrt{\frac{2 \cdot 15.0 \ m}{9.81 \ m/s^2}} = 3.02 \ s$[/tex]
The time interval associated with the 26.0 m of oscillation can be found using the equation for the period of a simple harmonic oscillator, which is:
[tex]$T = 2 \pi \sqrt{\frac{m}{k}}$[/tex]
where $m$ is the mass of the object and k is the spring constant.
In this case, the mass of the object is 64.0 kg, and the spring constant is the force of gravity acting on the jumper, which is [tex]$mg = 64.0 \ kg \cdot 9.81 \ m/s^2 = 628.64 \ N/m$[/tex]
Therefore, the time interval associated with the oscillation can be calculated as follows:
[tex]$T = 2 \pi \sqrt{\frac{64.0 \ kg}{628.64 \ N/m}} = 2.01 \ s$[/tex]
The total time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion is the sum of the time intervals for the free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].
To learn more about harmonic oscillator
https://brainly.com/question/26114128
#SPJ4
Which of the following changes would make the water balloon more likely to pop? (Ignore effects of convection within the fluid.)
a) Use a thicker balloon.
b) Use a liquid that has a higher heat capacity than water.
c) Use a liquid that has a lower heat capacity than water.
d) Use a thinner balloon.
The changes that would make the water balloon more likely to pop is: to use a liquid that has a lower heat capacity than water to use a thicker balloon. The correct options are B and C.
What is heat capacity? Heat capacity or also known as thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature.
So, Using a liquid that has a lower heat capacity than water and using a thicker balloon will make the water balloon more likely to pop. We know now that heat capacity or specific heat is the amount of heat per unit mass that is required to raise the temperature by 1°C.
This is helpful in determining the processing temperatures along with the amount of heat required for processing and could be helpful for differentiating between two polymeric composites.
Learn more about heat capacity at: http://brainly.com/question/29313493
#SPJ4
Which of the following scenarios best describes what Erik Erikson thought someone might experience in early adulthood?p
The clearest example of what Erik Erikson believed a person might go through in early adulthood Mohammed has tried dating a few times but has not had much luck, so he has decided to give it up.
The way in which Erikson's theory handled development over the lifetime, including old age, set it apart from many others. We are driven to investigate intimate connections as young people because we want to build our own relationships. Young adulthood, the sixth stage in Erikson's theory of psychosocial development, occurs between the ages of 18 and 40. The clearest example of what Erik Erikson believed a person might go through in early adulthood Mohammed has tried dating a few times but has not had much luck, so he has given up.
Learn more about Adulthood
brainly.com/question/10477610
#SPJ4
true/false. . dynamic viscosity relates to deformation rate of a uid in response to a shear stress. in class, we discussed how it changes with temperature for liquids and gases. here, we present dierent ways to model the temperature-viscosity relationship.
true, The rate at which a fluid deforms in response to a shear stress is referred to as its dynamic viscosity. It is a measurement of a fluid's resistance to deformation, and the Greek letter mu () is frequently used to represent it.
Absolute viscosity, commonly referred to as dynamic viscosity, is a measurement of a fluid's flow resistance. The amount of internal friction that a fluid possesses dictates how much force is necessary to move the fluid; this is a characteristic of the fluid. The amount of internal friction and force needed to move a fluid increases with its viscosity. The Greek letter mu () is frequently used to represent dynamic viscosity, which is quantified in units called pascal-seconds (Pas). It depends on temperature and pressure, and it may be influenced by things like the presence of suspended particles, dissolved gases, and fluid flow velocity. Pressure decreases may be calculated using dynamic viscosity.
learn more about dynamic viscosity here:
https://brainly.com/question/30264313
#SPJ4
What cause-and-effect relationships identified in the spring-loaded cart can be applied to the rocket sled?
Cause
Effect
1. Increase in thrust: The same cause-and-effect relationship applies to a rocket sled. When the thrust of the rocket sled is increased, it will cause an increase in the acceleration of the sled.
What is acceleration?Acceleration is the rate at which an object's speed or velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. Acceleration can be caused by a number of factors, including forces, changes in gravity, or changes in direction. Acceleration is the second derivative of velocity with respect to time, or the rate of change of the velocity vector.
This is because the increased thrust generates more force, which in turn causes the sled to accelerate faster.
2. Increase in weight: The same cause-and-effect relationship applies to a rocket sled. When the weight of the rocket sled is increased, it will cause a decrease in the acceleration of the sled. This is because the increased weight will require more force to accelerate the sled, thus resulting in a slower acceleration.
To learn more about acceleration
https://brainly.com/question/460763
#SPJ1
mass of gold is 4.295 g leaf of 3.449 um thickness
(a) The area of the leaf is 0.064 m².
(b) The length of the fiber is 10,359.2 m.
What is the area of the leaf?
The area of the leaf is calculated from the volume of the leaf, while the volume of the leaf is calculated from the density and mass of the leaf.
V = m / ρ
where;
V is the volume of the gold leafm is the mass of the gold leafρ is the density of the gold leafV = ( 4.295 g ) / ( 19.32 g/cm³ )
V = 0.22 cm³ = 0.22 x 10⁻⁶ m³
Ah = V
A = V / h
where;
h is the thickness of the leadA is the area of the leafA = ( 0.22 x 10⁻⁶ m³ ) / ( 3.449 x 10⁻⁶ m )
A = 0.064 m²
The length of the fiber is calculated as follows;
V = πr²h
h = V / πr²
h = ( 0.22 x 10⁻⁶ m³ ) / ( π x 2.6 x 10⁻⁶ m x 2.6 x 10⁻⁶ m )
h = 10,359.2 m
Learn more about area here: https://brainly.com/question/25292087
#SPJ1
a heat engine that accepts heat from and rejects heat to the same thermal energy reservoir is an example of a device that violates which of the following? multiple choice question. first law clausius statement of the second law kelvin-planck statement of the second law
A heat engine is in violation of the second rule of thermodynamics if it claims to have a thermal efficiency higher than the Carnot efficiency.
In science, what is an energy?Energy is characterized as having the "ability to accomplish work, which is the capacity to apply a force sufficient to move an object." Despite this unclear definition, the concept is essentially quite straightforward: electricity merely refers to the force that drives objects. Potential and kinetic energy are the two different categories.
Easy definition of energyThe ability to perform work is the most basic definition of energy. Things alter and move because of energy. It comes in many different shapes and is all around us. Cooking food requires energy.
To know more about Energy visit:
https://brainly.com/question/1932868
#SPJ4
forensic science 3.05 make a claim about the electrophoresis results and a possible match to a suspect. then, provide evidence and reasoning to support your claim
A recurrent offender is present at work when two crime scene profiles match. This DNA evidence may be used by the police to support other evidence and aid in a criminal prosecution.
Complete DNA profiles provide extremely reliable matches and can be used to prove a suspect's guilt or innocence in a criminal case. After being put into a gel and exposed to an electrical field, the DNA fragments are electrophoretically sorted into different bands. To make these bands visible to imaging methods, a radioactive dye can be used to color them.
DNA fingerprints are produced via gel electrophoresis using samples taken from crime scenes and suspects. A similarity between samples identifies the criminal suspect.
Learn more about electrophoresis Visit: brainly.com/question/20782240
#SPJ4
When two crime scene profiles match, a repeat offender is present at work. The authorities may use this DNA proof to back up other evidence and build a criminal case.
A suspect's guilt or innocence in a criminal case can be established using whole DNA profiles, which offer incredibly reliable matches. The DNA fragments are electrophoretically separated into distinct bands after being placed in a gel and subjected to an electrical field. These bands can be coloured with a radioactive dye to make them apparent to imaging techniques.
Gel electrophoresis is used to create DNA fingerprints from samples obtained from crime scenes and suspects. The criminal suspect is identified by similarities between samples.
For such more question on crime scene
https://brainly.com/question/27031267
#SPJ4
using the numbered direction arrows shown, indicate (by number) which direction arrow best represents the direction of the quantities listed below. if the quantity has zero magnitude or cannot be determined, indicate this with a 9 or 10, respectively.
The position vector at position D is shown by arrow 1, the change in position (displacement) between positions D and F is shown by arrow 2, and the average net force and change in velocity between positions D and F cannot be calculated.
Arrow 1 is a representation of the position vector for position D.
Arrow 2 illustrates the shift (position change) between positions D and F.
Arrow 3 illustrates the undeterminable velocity change between positions D and F.
Arrow 4 denotes the change in momentum from position D to position F. arrow 5 illustrates the indeterminable average net force between positions D and F. The vector's position is.
Arrow 6 displays position E.
Arrow 7 illustrates the positional shift between locations D and E.
Arrow 8 illustrates the difference in velocity between positions D and E.
Arrow 9 depicts the difference in momentum between positions D and E.
The indeterminable average net force between positions D and E is symbolized by arrow 10 and cannot be calculated.
To learn more about vectors at
https://brainly.com/question/29740341?referrer=searchResults
#SPJ4
The question is -
Using the numbered direction arrows shown, indicate (by number) which direction arrow best represents the direction of the quantities listed below. If the quantity has zero magnitudes or cannot be determined, indicate using the corresponding number listed below. The position vector at location D _____ The change in position (the displacement) between location D and location F _____ The change in velocity between location D and location F _____ The change in momentum between location D and location F _____ The average net force between location D and location F _____ The position vector at location E _____ The change in position (the displacement) between location D and location E _____ The change in velocity between location D and location E _____ The change in momentum between location D and location E _____ The average net force between location D and location E.
Which of the following accurately details the relationship between wavelength of illumination, lens quality, magnification, and the limit of resolution for light microscopy?A) As shorter wavelength illumination and better quality lenses are used, magnification will increase and the limit of resolution will decrease.B) As shorter wavelength illumination and better quality lenses are used, magnification will decrease and the limit of resolution will decrease.C) As shorter wavelength illumination and better quality lenses are used, magnification will increase and the limit of resolution will increase.D) Magnification and limit of resolution are independent of wavelength of illumination and lens quality for light microscopy.
C) As shorter wavelength illumination and better quality lenses are used, magnification will increase and the limit of resolution will increase.
What is wavelength illumination?Wavelength illumination is a way of measuring the intensity of a light source in terms of the wavelength of the light being emitted.
Light microscopes use light of different wavelengths and high-quality lenses to magnify and enhance images. Shorter wavelength illumination, such as UV light, can provide greater resolution because it has a higher frequency than longer wavelengths, such as visible light. Additionally, higher quality lenses provide greater magnification and allow for a larger field of view. Thus, as shorter wavelength illumination and better quality lenses are used, magnification will increase and the limit of resolution will also increase.
To learn more about wavelength illumination
https://brainly.in/question/35746
#SPJ4
3. calculate rab a. for the resistor network below (10 points) b. for the modified resistor network below (10 points)
To calculate electrical resistance for a resistor network first you have to check whether the resistors are in series or parallel connection and then apply the formula of resistance.
R= V/I where V is the potential difference across the conductor (in volts) and I is the current through the conductor (in amperes).
Electrical resistance is the property of an electrical conductor to oppose the flow of electric current. All materials have their own electrical resistance and is represented by R and its SI unit is ohm.
Resistance can be calculated using the Ohm's law. It is defined as the ratio of the applied voltage to the current.
To calculate the total resistance of a network in series connection,
Total resistance = R₁+ R₂+ R₃
To calculate the total resistance of a network in parallel connection,
Total resistance = 1/R₁+ 1/R₂+ 1/R₃
Learn more about total resistance here:
https://brainly.com/question/16465349
#SPJ4
Which of the following statements describes meta-analysis
Meta-analysis includes all of these such as systematic inclusion and exclusion criteria for studies, multiple, systematic searches to identify studies which answer a focused question, only quantitative studies are included in this. Thus, the correct option is B.
What is Meta-analysis?A meta-analysis is a statistical analysis which combines the results of multiple scientific studies. Meta-analyses of anything can be performed when there are multiple scientific studies available which are addressing the same question, with each of the individual study reporting measurements which are expected to have some degree of error in it.
The subjects from all the studies were pooled and statistically analyzed to determine the effect of the one thing such as relationship between wearing sunscreen and melanoma. This meta-analysis has been found to show a 50% reduction in the melanoma diagnosis among the sunscreen-wearers.
Therefore, the correct option is B.
Learn more about Meta-analysis here:
https://brainly.com/question/29442056
#SPJ1
Your question is incomplete, most probably the complete question is:
Which of the following describe meta-analysis?
A. Systematic inclusion and exclusion criteria for studies
B. All of these
C. Multiple, systematic searches to identify studies that answer a focused question
D. Only quantitative studies are included
E. None of these
A team in Quebec is playing ice baseball. A 72 kg player who is initially at rest catches a 145 g ball traveling at 18 m/s. If the player's skates are frictionless, how much time is required for him to glide 5 m after catching the ball?
The time required for the player to glide 5m after catching the ball would be 0.073 seconds.
What is conservation of momentum principle?
The conservation of momentum principle states that in an isolated system (one in which there are no external forces acting on it), the total momentum of the system will remain constant. This principle is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.
To calculate the time required for the player to glide 5m after catching the ball, we need to use the conservation of momentum principle.
The initial momentum of the system (player + ball) is 0, since the player is at rest. After catching the ball, the final momentum of the system is (72 kg) (0 m/s) + (0.145 kg) (18 m/s) = 2.61 kg m/s.
To find the final velocity of the player, we can use the equation:
Final momentum = Initial momentum + Impulse
where Impulse = force x time
The force is equal to the change in momentum of the system divided by the time it takes for the change to occur.
So, Impulse = (2.61 kg m/s - 0) / t
Also, the impulse is equal to the mass of the player multiplied by the change in velocity of the player.
So, (72 kg) (change in velocity of the player) = (2.61 kg m/s - 0) / t
Now we can calculate the time it takes for the player to glide 5m.
change in velocity = final velocity - initial velocity = 5/t
(72 kg) (5/t) = 2.61 kg m/s
t = (2.61 kg m/s) / (72 kg × 5 m/t) = 0.073 seconds
So, the player will glide 5m after catching the ball in 0.073 seconds.
To know more about law of conservation of energy, visit:
https://brainly.com/question/29775341
#SPJ4
1. A 6-kg bowling ball sits on top of a building that is 120 meters tall.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
Mass = GPE=mgh
Gravity (g) = 9.8 m/s2
Height =
2. A 3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.
Circle one: (KE) / GPE / both
Show your work for finding the values of each type of energy the object has:
KE GPE=mgh
Mass = Mass =
Velocity = Gravity (g) = 9.8 m/s2
Velocity2= Height =
KE = ½ (M) (V)2 GPE=mgh
3. A 4-kg bowling ball rolls at a speed of 15 m/s on the ground.
Circle one: (KE) / GPE / both
Show your work for finding the values of each type of energy the object has:
KE KE = ½ (M) (V)2
Mass =
Velocity =
Velocity2=
4. A 15-kg child is tossed up into the air by her parent. The child is 2.5 meters off the ground traveling 3 m/s.
Circle one: KE / GPE / (both)
Show your work for finding the values of each type of energy the object has:
KE GPE
Mass = Mass =
Velocity = Gravity (g) = 9.8 m/s2
Velocity2= Height =
KE = ½ (M) (V)2 GPE=mgh
KE + GPE =
(1) The gravitational potential energy of the bowling ball is 7,056 J.
(2)The potential energy and kinetic energy of the bowling ball are 2,205 J and 37.5 J respectively.
(3) The kinetic energy of the bowling ball is 450 J.
(4) The potential energy and kinetic energy of the child re 367.5 J and 67.5 J respectively.
What is the gravitational potential energy of the bowling ball?The gravitational potential energy of the bowling ball is calculated by applying the following formula;
P.E = mgh
where;
m is the mass of the objecth is the heightg is acceleration due to gravityP.E = ( 6kg x 9.8 m/s² x 120 m )
P.E = 7,056 J
(2) The potential energy and kinetic energy of the bowling ball is calculated as follows;
P.E = (3 x 9.8 x 75 )
P.E = 2,205 J
K.E = ¹/₂ mv²
K.E = ¹/₂ ( 3 ) x (5²)
K.E = 37.5 J
(3) The kinetic energy of the bowling ball is calculated as follows;
K.E = ¹/₂ mv²
K.E = ¹/₂ ( 4 ) x (15²)
K.E = 450 J
(4) The potential energy and kinetic energy of the child is calculated as follows;
P.E = (15 x 9.8 x 2.5 )
P.E = 367.5 J
K.E = ¹/₂ mv²
K.E = ¹/₂ ( 15 ) x (3²)
K.E = 67.5 J
Learn more about potential energy here: https://brainly.com/question/1242059
#SPJ1
for each set of questions below think about which quantities cant change when a parallel plate is isolated
What is the capacitance of the parallel plate:
The capacitance of the parallel plate cannot change when it is isolated because it is determined by the physical characteristics of the plate, such as its area, distance between plates, and permittivity of the material between them. These characteristics do not change when the plate is isolated.
Capacitance is a measure of the ability of a component or system to store electrical energy. It is the ratio of the electric charge on a conductor to the potential difference between its ends. The unit of capacitance is the Farad (F). Capacitors are components that are used to store electrical energy and are found in many electronic circuits. They consist of two conductive plates separated by an insulating material called a dielectric.
To learn more about capacitance
https://brainly.com/question/27753307
#SPJ4
in a vacuum, light travels 300,000 km every second. examine the following figure, which shows how long it takes for light to travel particular distances, and then scroll down to the question at the end.
If the Sun's light suddenly went out, we would not notice it for at least 8 minutes from Earth. When we look at the Andromeda Galaxy, we are seeing it as it was millions of years ago. At the speed of light, communications between Earth and astronauts on the Moon would be significantly delayed.
What is vacuum?A vacuum is a volume that is devoid of substance, often known as 'free space'. Only partial vacuums are achievable in practice. A vacuum is a space in which there is no matter or where the pressure is so low that any particles in the space have no effect on any activities that are taking place. It is a state that is far below normal atmospheric pressure and is measured in pressure units (the pascal). A vacuum is defined in science as a space devoid of substance or air. That's the simple definition, however there are always some particles of stuff in a vacuum, but far fewer than the air you're inhaling.
Here,
If the Sun's light were abruptly extinguished, we would not notice it for more than 8 minutes from Earth. When we look at the Andromeda Galaxy, we are gazing back in time to how it appeared millions of years ago. There would be a substantial delay in communications between Earth and astronauts on the Moon at the speed of light.
To know more about vacuum,
https://brainly.com/question/24189092
#SPJ4
Can a charged particle have a net negative charge of 6.4 x 10-19
C? Take the elementary charge (the charge of a single electron) to
be -1.6 x 10 19 C.
No, because the particle has a positive charge.
Yes, because the particle has excess charges.
0/1 pts
No, because the particle has deficiency of charges
(missing electrons)
Yes, because the particle has an integer number of excess
electrons.
By dividing an object's charge by its basic charge, one can calculate the quantity of extra electrons (or protons, in the case of positive charges), in a system.
What material that has an excess of electrons?When there are lots of free electrons in a material, it is said to have high electron mobility, but when there are few or no free electrons, it is said to have low electron mobility. Here are some typical illustrations of conductors and insulators: Conductors.It indicates that metals contain extra electrons in their outermost shell that are free to move about. These extra electrons act as charge carriers and are physically transferred when a current is running.To convert, multiply the net charge, Q, by the factor 1.6 x 10 x 19 to obtain the charge's value in basic charge units. This is also equivalent to how many extra electrons are present on the thing.To learn more about charge refer to:
https://brainly.com/question/25922783
#SPJ1
Suppose you used a hot pot to convert a 150 g piece of ice that was initially at -15°C into liquid water at 50°C.
a. Represent this process in one complete energy-system diagram covering the entire interval. b. How much heat is added to complete this entire process?
c. if your hot pot has a power rating of 600 watts, show how to find how long it will take to complete the process. (make sure you are comfortable using standard units of energy, and that you understand the relation of power to energy. hint: what are watts?)
(a) The energy-system diagram is shown in the picture attached.
(b) The heat energy added is 86,295 Joule.
(c) It takes 144 seconds to complete the process.
We solve the problem with the formula for heat energy.
What is heat?Heat is the energy that is transferred from higher to lower temperature. The quantity of heat energy (also called thermal energy) can be calculated by
Q = mcΔT, when there is change in temperature.Q = mL, when there is no change in temperature.A 150 g piece of ice is converted from -15°C to 50°C in a hot pot. The power rate is 600 Watts.
a. Make the energy-system diagram!
b. Total heat energy added! (Q total)
c. Time to complete the process! (t)
The diagram picture is shown in the attachment. The piece of ice is heated from -15 degrees Celsius to zero by the energy of Q₁. When it reaches zero temperature, the ice is melted by the energy of Q₂. After all the solid ice melts, the liquid water continues to rise in temperature up to 50 degrees Celsius by the energy of Q₃.
The scientific data shows
Specific heat of ice, c_ice = 0.5 cal/g°C.Specific heat of water, c_water = 1 cal/g°C.Laten heat of fusion, L_fusion = 80 cal/g.1 calories = 4.184 JouleThe total heat energy absorbed is
Qt = Q₁ + Q₂ + Q₃
Qt = mcΔT (ice) + mL (melting) + mcΔT (water)
Qt = m(c_ice × ΔT + L_fusion + c_water × ΔT)
Qt = 150[0.5 × (0-(-15)) + 80 + 1 × (50-0)]
Qt = 150[7.5) + 80 + 50]
Qt = 150[137.5]
Qt = 20,625 calories
Convert the unit from calories to Joule!
Qt = 20,625 × 4.184 Joule
Qt = 86,295 Joule
The time taken to complete the entire process would be
P = Q/t
600 = 86,295/t
t = 86,295/600
t ≈ 144 seconds
Hence, the process in the diagram as shown in the picture attached has the total heat energy of 86,295 Joule. It will take 144 seconds to complete the process.
Learn more about heat energy here:
brainly.com/question/898227
#SPJ4
Two satellites, A and B, are in different circular orbits about the earth. The orbital speed of satellite A is eighty-three times that of satellite B. Find the ratio (TA/TB) of the periods of the satellites. Answer the one above ^^^^^^^^^^^ But I did a example with this one Two satellites, A and B, are in different circular orbits about the earth. The orbital speed of satellite A is forty times that of satellite B. Find the ratio (TA/TB) of the periods of the satellites. And the answer was 1.56e-05
When the orbital speed of satellite A is eighty-three times that of satellite B, the period ratio Ta/Tn equals 83:1.
What is orbital speed?The orbital speed of an astronomical body or object in a gravitationally bound system is the speed at which it circles around the barycenter or, if one body is substantially more massive than the other entities in the system combined, its speed relative to the center of mass of the most massive body. The object's orbital speed is the rate at which it circles around the barycenter of a system, which is generally a big body. The earth's orbital speed around the sun is 108,000 km/h. The orbital speed of a planet varies with its distance from the Sun. The greater the strength of the Sun's gravitational attraction on a planet, the quicker it travels.
Here,
The orbit of the two satellites is circular.
Also, Orbital speed of A is 2 times the orbital speed of B.
vₐ=2vₙ
v=2T
vₐ=2Tₐ
2vₙ=2Tₐ
vₙ=2Tₙ
Tₐ/Tₙ=83/1
The ratio Tₐ/Tₙ of the periods of the satellites is 83:1 when the orbital speed of satellite A is eighty-three times that of satellite B.
To know more about orbital speed,
https://brainly.com/question/13260980
#SPJ4
The acceleration of a particle is directly proportional to the square of the time t. When t=0, the particle is at x=24m. Knowing that at t=6s, x=96m and v=18m/s, express x and v in terms of t.
Answers are: x(t) = t^4/108 + 10t + 24, v(t) = t^3/27 + 10
Need to see the solution to understand.
The position and velocity of the particle are [tex]x(t) = 2t^2 + 24[/tex] and [tex]v(t) = 4t[/tex]
The problem states that the acceleration of a particle is directly proportional to the square of the time, which means that the equation for acceleration (a) is of the form [tex]a = k*t^2[/tex], where k is a constant.
Given that the position of the particle at t = 0 is x = 24m, we can use this to find the initial velocity (v0) using the equation: [tex]x = x0 + v0t + 1/2a*t^2[/tex].
Since we know that x = 24m at t = 0, we can substitute these values into the equation and get:
[tex]24 = 24 + v00 + 1/2k*0^2[/tex]
This simplifies to v0 = 0.
Now, we can use the information that at t = 6s, x = 96m and v = 18m/s to find the value of k. We know that [tex]x = x0 + v0t + 1/2at^2[/tex] and v = v0 + at.
So we can substitute these values into the equation and get:
[tex]96 = 24 + 0 + 1/2k6^2 = 24 + 1/2k36[/tex]
18 = 0 + k*6
Solving the above two equations, we get k = 4.
So the equation for acceleration is [tex]a = 4*t^2[/tex].
We can use this equation to find the equations for position and velocity by using the following formulas:
[tex]x(t) = x0 + v0t + 1/2at^2[/tex]
[tex]v(t) = v0 + at[/tex]
Substituting the values we know, we get:
[tex]x(t) = 24 + 0 + 1/2*(4t^2) = 2t^2 + 24[/tex]
[tex]v(t) = 0 + 4t = 4t[/tex]
So, the position and velocity of the particle are given by [tex]x(t) = 2t^2 + 24[/tex]and [tex]v(t) = 4t[/tex] respectively.
To learn more problems on position and velocity:
https://brainly.com/question/14298562
#SPJ4
if the car decelerates uniformly along the curved road from 25 m>s at a to 15 m>s at c, determine the acceleration of the car at b.
If the car decelerates uniformly along the curved road from 25 m>s at a to 15 m>s at c. The acceleration of the car at b is 1.18m/s²
We are given the speed of the car at point A is Va= 25 m/s, and the speed of the car at point C is Vc= 15 m/s.
Calculating the car's acceleration at B is the task at hand.We have the distance between points A and B as dAB = 250 m
We have the distance between points A and B as dAC = 250 m + 50 m= 300m
We have the distance between points A and B as dBC = 50m
We have the radius of the track as βB = 300m
The formula to calculate the tangential acceleration of the car is,
(vc)² = (vA)² + 2at (dAC)
Substitute the values in the above expression.
(15 m/s)² = (25 m/s)² + 2at (300m)
at = - 0.67 m/s²
The formula to calculate the velocity of the car at point B is,
(vB)²= (vA)² + 2at (dAB)
Substitute the values in the above expression.
(vB)²= (25 m/s)² + 2( - 0.67 m/s) (250m)
vB = 17.03 m/s
The formula to calculate the normal acceleration of the car is,
an = (vB)²÷β B
Substitute the values in the above expression.
an= (17.03m/s)² ÷ 300m
an = 0.97 m/s²
The formula to calculate the acceleration of the car is,
a=√ (at)² + (an)²
Substitute the values in the above expression.
a = √ (- 0.67 m/s)² + (0.97 m/s²)²
a = 1.18 m/s²
Therefore, the answer is 1.18 m/s²
To know more about acceleration:
https://brainly.com/question/28601338
#SPJ4
you observe that a negatively charged plastic pen repels a charged piece of magic tape. you then observe that the same piece of tape is repelled when brought near a small metal sphere. you are wearing rubber soled shoes, and you touch the metal sphere with your hand. after you touch the metal sphere, you observe that the tape is attracted to the metal sphere. which of the following statements could be true. list all that apply, sep
The correct statements are options given below:
(The complete question is attached below)
According to the statement there is a force of repulsion between the two objects. Remember that two objects must have the same charge so that they repel each other.In this way if the tape is repelled by a plastic pen that is negatively charged, this allows us to appreciate that the tape is also negatively charged. Now if the tape repels the sphere, therefore the sphere is also negatively charged.Under these considerations the correct answers would be
2. Sodium ions from the salt water on your hand moved onto the sphere
4. The excess negative charge from the sphere spread out all over your body
6. Electrons from the sphere moved into the salt water on your skin, where they reacted with sodium ions
7. After you touched it, the metal sphere was very nearly neutral.
To know more about charges visit:
https://brainly.com/question/29814398
#SPJ4
rank the six combinations of electric charges on the basis of the electric force acting on q1 . define forces pointing to the right as positive and forces pointing to the left as negative. rank in increasing order by placing the most negative on the left and the most positive on the right. to rank items as equivalent, overlap them.
Smallest are: q1 = +1 nc, q2 = +1 nc, q3 = +1 nc and q1 = -1 nc, q2 = -1 nc, q3 = -1nc
Third Largest: q1 = +1 nc, q2 = +1nc, q3 = -1 nc
Second Largest: q1 = +1 nc, q2 = -1 nc, q3 = +1 nc
Largest : q1 = +1 nc, q2 = -1 nc, q3 = -1 nc and q1 = -1 nc, q2 = +1 nc, q3 = +1 nc
(Refer to image)
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative (commonly carried by protons and electrons respectively). Like charges repel each other and unlike charges attract each other.The electrostatic force between 2 charges is; F = k•q1•q2/r²Where r is the distance between the 2 charges q1 and q2 and k is coulombs constant.
Thus;F ∝ q1•q2/r²
The net force on the charge q1 is the sum of the forces on charge q2 and q3.If the two charges are opposite, the force is an attractive force while if the two charges are similar, the force is a repulsive force.Thus, if the combination has same type of charges, i.e;(+1,+1,+1) or (-1,-1,-1), the force will be very small.
So, now the order of forces from smallest to largest is;
Smallest are: q1 = +1 nc, q2 = +1 nc, q3 = +1 nc and q1 = -1 nc, q2 = -1 nc, q3 = -1nc
Third Largest: q1 = +1 nc, q2 = +1nc, q3 = -1 nc
Second Largest: q1 = +1 nc, q2 = -1 nc, q3 = +1 nc
Largest are: q1 = +1 nc, q2 = -1 nc, q3 = -1 nc and q1 = -1 nc, q2 = +1 nc, q3 = +1 nc
To know more about charges visit:
https://brainly.com/question/17482950
#SPJ4
from the top of a building, object 1 with mass m is thrown straight downward, and object 2 (also with mass m ) is thrown horizontally. both are thrown with the same speed. compare the speeds with which the objects hit the ground. from the top of a building, object 1 with mass is thrown straight downward, and object 2 (also with mass ) is thrown horizontally. both are thrown with the same speed. compare the speeds with which the objects hit the ground. object 1 hits the ground with a greater speed. object 2 hits the ground with a greater speed. both objects hit the ground with the same speed.
They'll be moving at the same speed when they reach the street.Weight (W), which is a force exerted on all objects on Earth by gravity, is a force.
Identify the speed?Weight (W), which is a force exerted on all objects on Earth by gravity, is a force. A body can only accelerate through gravity (g) when it is falling freely. Because of this, velocity increases.
Weight (W), which is a force exerted on all objects on Earth by gravity, is a force.
As a result of gravity, both objects' velocities will alter.
This equation yields the same velocity for both items when one is hurled up and the other down:
where v is the end speed, v0 is the starting speed, h is the height difference between the building and the street, and g is the acceleration brought on by gravity.
Assuming upward speed to be positive.
They'll be moving at the same speed when they reach the street.
To learn more about speed refer to:
https://brainly.com/question/13943409
#SPJ4
An ideal gas is contained in a cylinder of fixed length and diameter. Eighty joules of heat is added while the piston is held in place. The work done by the gas on the walls of the cylinder is
A. less than 80 J
B. 80J
C. not spesified by the information given.
D. 0J
E. more than 80J
The answer is C. Option C is the correct option. Not Specified by the Information Given.
The amount of work done by the gas on the walls of the cylinder is not specified by the information given. The amount of work done by the gas on the walls of the cylinder depends on the pressure of the gas, the temperature of the gas, and the volume of the gas.
Since none of these parameters are specified, it is not possible to determine the amount of work done by the gas on the walls of the cylinder. However, it is possible to determine the change in internal energy of the gas. Since 80 J of heat was added to the gas, the change in internal energy of the gas is 80 J.
Learn more about ideal gas:
https://brainly.com/question/27870704
#SPJ4
select all that apply from the following list, select the characteristics of all heat engines. (check all that apply.) multiple select question. reject heat to a low-temperature sink reject heat to a high-temperature sink receive heat from a high-temperature source receive heat from a low-temperature source
Receive heat from a high-temperature source and reject heat to a low-temperature sink are the characteristics of all heat engines.
What is High-temperature sources?High-temperature sources are materials that can produce and sustain high temperatures. These sources can range from small, localized heating elements to large, complex nuclear reactors. Common high-temperature sources include fossil fuels, such as wood, coal, and oil, as well as nuclear and solar energy. High-temperature sources are used in a variety of applications, including power generation, heating and cooling, and manufacturing processes.
Heat engines transfer heat from a high-temperature source to a low-temperature sink, so they cannot reject heat to a high-temperature sink or receive heat from a low-temperature source.
To learn more about high-temperature source
https://brainly.com/question/14609181
#SPJ4
puck b has five times the mass of puck a . starting from rest, both pucks are pulled the same distance across frictionless ice by strings with the same tension. part a compare the final kinetic energies of pucks a and b . compare the final kinetic energies of pucks and . ka
Pack B has twice the mass of pack A, and thus twice the kinetic energy, but has the same final velocity as pack A.
a. The ultimate kinetic energy of an object is given by the formula KE = 1/2 × m × v². where m is the object's mass and v is its velocity. Since both pucks are pulled at the same distance by a string of the same tension, the final kinetic energy of both pucks will be the same. However, pack B has twice the mass of pack A, so the final kinetic energy is twice that of pack A. The final velocity of the
b. Object is given by the equation v = √(2 × KE / m). Both packs have the same final kinetic energy, but pack B has twice the mass of pack A, so the final velocity is √(2 × KE / mB) = √(2 × KE / (2 × mA)) = √(KE / mA ), which is the square root of the terminal velocity of pack A.
To learn more about kinetic energy at
https://brainly.com/question/26472013?referrer=searchResults
#SPJ4
The question is -
Puck B has twice the mass of puck A. Starting from rest, both pucks are pulled the same distance across frictionless ice by strings with the same tension a. Compare the final kinetic energies of pucks A and B. b. Compare the final speeds of pucks A and B.
A tuning fork with a frequency of 512 Hz is struck at the same time as a guitar string. If 24 beats are heard in
6.0 s, find the possible frequency or frequencies of the guitar string.
The possible frequencies of the guitar string are 488 Hz and 536 Hz.
What are the possible frequencies of the guitar string?
The possible frequency or frequencies of the guitar string is calculated by applying beat frequency formula.
Fb = Ft - Fg or
Fb = Fg - Ft
where;
Fb is the beat frequencyFg is frequency of the guitarFt is the frequency of the tuning forkFg = Ft - Fb
Fg = 512 Hz - 24 Hz
Fg = 488 Hz
Fg = Fb + Ft
Fg = 24 Hz + 512 Hz
Fg = 536 Hz
Learn more about beat frequency here: https://brainly.com/question/3086912
#SPJ1
The following 5 sodium control values in unit (mEq/L) were obtained:140, 135, 138, 140, 142Calculate the coefficient of variation?
The coefficient of variation for the 5 sodium control values is 1.61%.
What is coefficient?Coefficient is a numerical value used to express the magnitude of a physical quantity in relation to another physical quantity. It is a constant value used to convert one set of units to another set of units, or to express the relationship between two physical quantities.
The coefficient of variation (CV) is a measure of the variability of a set of values relative to its mean. To calculate the coefficient of variation, we need to calculate the standard deviation of the values.
Standard deviation = √((140-138.2)2 + (135-138.2)2 + (138-138.2)2 + (140-138.2)2 + (142-138.2)2 / 5)
Standard deviation = 2.22
Coefficient of variation = (Standard deviation/mean)*100
Coefficient of variation = (2.22/138.2)*100
Coefficient of variation = 1.61%
Therefore, the coefficient of variation for the 5 sodium control values is 1.61%.
To learn more about coefficient
https://brainly.com/question/29719172
#SPJ4
you are using a wrench to rotate a bolt around its center. consider all the forces in (figure 1), indicated by the arrows, to have the same magnitude. which of the following scenarios apply zero torque?
The following situations use no torque. C=D, A,B,E,C,D.
Describe a magnitude example.Size is referred to as magnitude. A automobile is traveling more quickly than a bike, for instance, when it comes to speed. In this case, the car is moving faster than the bike by a larger margin. It reveals the direction or size, whether absolute or relative, in which an object moves.
How big is a vector supposed to be?The vector's length determines its magnitude. The symbol for the vector's magnitude is a. To learn more about a vector's magnitude, see to its introduction. Vector magnitude formulas for two dimensions.
To know more about Magnitude visit:
https://brainly.com/question/15681399
#SPJ4
four charges are placed on the vertices of a square and one at its center. using the symmetry of the arrangement, determine the direction of the force on the positive charge q in figure above, give that :
qa=qb= +7.50nC and qc=qd = -7.50nC
a. up
b. down
c. left
d. right
The direction of the direction of the force on the positive charge q will be towards left.
Lets assume that the Q is at the center of a coordinate graph, qa = qb = +7.50 nC are in third and second quadrant and qc = qd = -7.50 nC are in first and fourth quadrant. Then
F = k[-qQ(r₀-r₁)/(r₀-r₁)³ + qQ(r₀-r₂)/(r₀-r₂)³ + qQ(r₀-r₃)/(r₀-r₃)³ + -qQ(r₀-r₄)/(r₀-r₄)³]
According to the vectors
F = kqQ/r²[-(i+j) + (-i+j) + (-i-j) + -(i-j)]
F = kqQ/r²[-i -j + -i + j + -i -j + -i + j]
F = kqQ/r²[-4I]
I vector represent x-axis which is negative towards the left. As we can see that the resultant vector is in the direction of negative i-vector. As we assumed that the Q is at the center of the coordinate graph, so the direction of force will be left to the charge Q. Hence the correct option is C.
To know more about force, here
https://brainly.com/question/13191643
#SPJ4