Answer:
Explanation:
a ) x ( t ) = t³ / 3 - t² + t
v = dx / dt = 3 t² / 3 - 2 t + 1 = t² - 2 t + 1
b ) lizard is at rest , v( t ) = 0
t² - 2 t + 1 = 0
( t - 1 )² = 0
t = 1
c )
velocity is positive when
t² - 2 t + 1 > 0
( t - 1 ) ² > 0
Here we see that LHS is a square so it is always positive whatever be the value of t
So velocity is always positive or lizard is always moving in positive x direction .
d ) It never moves in negative x direction .
e )
a ( t ) = dv / dt = 2t - 2
t = 1
so it has zero acceleration at t = 0 .
An electronic line judge camera captures the impact of a 57.0-g tennis ball traveling at 32.2 m/s with the side line of a tennis court. The ball rebounds with a speed of 21.6 m/s and is seen to be in contact with the ground for 3.94 ms. What is the magnitude of the average acceleration of the ball during the time it is in contact with the ground
Answer:
average acceleration is 1.365 × [tex]10^{4}[/tex] m/s²
Explanation:
given data
initila speed u = -32.2 m/s
final speed v = 21.6 m/s
time taken t = 0.00394 s
solution
we get here average acceleration that will be express as
v = u + at ..........................1
put here value and we get
21.6 = -32.2 + a × 0.00394
solve it we get
a = 1.365 × [tex]10^{4}[/tex] m/s²
so average acceleration is 1.365 × [tex]10^{4}[/tex] m/s²
You stand at the top of a cliff while your friend stands on the ground below you. You drop a ball from rest and see that it takes 1.7s for the ball to hit the ground below. Your friend then picks up the ball and throws it up to you, such that it just comes to rest in your hand. What is the speed with which your friend threw the ball
Answer:
16.7m/s
Explanation:
Using v= u+ at
V = final velocity. U = initial velocity
So since the two movements are the same they will return with the same speed they went up
Then final velocity v= 0
So
0:= u +-9.8 x 1.7
U= 16.7m/s
A corvette starts from rest and travels 69.0 meters in 50 s. What is its acceleration?
Answer:
0.0552 m/s²
Explanation:
Given:
Δx = 69.0 m
v₀ = 0 m/s
t = 50 s
Find: a
Δx = v₀ t + ½ at²
69.0 m = (0 m/s) (50 s) + ½ a (50 s)²
a = 0.0552 m/s²
27.
In a graph showing how temperature of a material changes over time, temperature
change is the:
A. dependent variable
C. variable with the smallest range
B. independent variable
D. variable with the largest range
Answer:
A. Dependent variable
Explanation:
In a graph showing how temperature of a material changes over time, temperature is taken on y-axis and time is taken on x-axis. It shows how temerature altered as the time changes.
In temperature-time graph, temperature is directly dependent on time. With the increase in time, temperature rises, falls or remains constant. It implies that temperature is dependent variable that depend on time.
Hence, the correct option is (A).
(b) If you decrease the length of the pendulum by 25%, how does the new period TN compare to the old period T?
Answer:
The new period will be reduced by 50%
Explanation:
The period of pendulum is given by;
[tex]T= 2\pi\sqrt{\frac{L}{g} }\\\\\frac{T}{2\pi} = \sqrt{\frac{L}{g} }\\\\(\frac{T}{2\pi} )^2 = {\frac{L}{g}}\\\\\frac{T^2}{4\pi ^2} = {\frac{L}{g}}\\\\T^2(\frac{g}{4\pi ^2}) = L\\\\ \frac{g}{4\pi ^2}= \frac{L}{T^2}\\\\\frac{L_1}{T_1^2} = \frac{L_2}{T_2^2}[/tex]
When the length is decreased by 25%, the new length L₂ is given by;
L₂ = 25/100(L₁)
L₂ = 0.25L₁
[tex]\frac{L_1}{T_1^2} = \frac{L_2}{T_2^2}\\\\T_2^2 = \frac{T_1^2L_2}{L_1} \\\\T_N^2 = \frac{T^2(0.25L_1)}{L_1}\\\\ T_N^2 =0.25T^2\\\\T_N = \sqrt{0.25T^2}}\\\\T_N = 0.5 T[/tex]
Thus, the new period will be reduced by 50%
Which of the following is the best description of a gaseous substance?
It's the result of a chemical reaction involving two or more elements.
It has no definite shape or volume and will expand indefinitely.
It holds its shape without outside restraint.
It has no shape of its own but has a definite volume.
The best description of a gaseous substance is : (B). It has no definite shape or volume and will expand indefinitely.
Meaning of a gaseous substanceA gaseous substance can be defined as a substance that is gaseous in nature or exhibit gaseous properties
A gaseous substance is just like a gas that its particles have unrestricted movement and the force of attraction between the particles are very weak or negligible.
In conclusion, The best description of a gaseous substance is : (B). It has no definite shape or volume and will expand indefinitely.
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the two forces acting on a boat or some other floating object _______are and gravity
Answer:
The two forces acting on a boat or some other floating object are buoyancy and gravity
Answer: buoyant forceExplanation:two forces acting on a boat or some other floating object are buoyant force and gravityhi friend your answerI hope it will be helpful for you
mark as brainest answer
thank you
If an automobile with a velocity of 4.0 m/s accelerates at a rate of 4.0 m/s2
for 2.5 s, what is the final velocity?
Answer:
V=u+at
=4+4*2.5
=14m/s
Explanation:
Initial velocity =4m/s
acceleration =4m/(second) squared
time =2.5 seconds
v=u+at
v=4+4*2.5
v=14m/s
Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta.
Answer:
[tex]2cos^2(\theta) - 1 = cos(2\theta)[/tex]
Explanation:
Given
[tex]2cos^2(\theta) - 1[/tex]
Required
Simplify
In trigonometry:
[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
So; the given expression becomes
[tex]2cos^2(\theta) - (sin^2(\theta) + cos^2(\theta))[/tex]
Open Bracket
[tex]2cos^2(\theta) - sin^2(\theta) - cos^2(\theta)[/tex]
Collect Like Terms
[tex]2cos^2(\theta) - cos^2(\theta)- sin^2(\theta)[/tex]
[tex]cos^2(\theta)- sin^2(\theta)[/tex]
In trigonometry:
[tex]cos(\theta + \theta) = cos^2(\theta)- sin^2(\theta)[/tex]
This implies that:
[tex]cos^2(\theta)- sin^2(\theta) = cos(\theta + \theta)[/tex]
=
[tex]cos(\theta + \theta)[/tex]
[tex]cos(2\theta)[/tex]
Hence:
[tex]2cos^2(\theta) - 1 = cos(2\theta)[/tex]
c) A sample of substance of volume 10 cm3 was brought back to Earth from the Moon.
The weight of the sample on the Moon was 0.13 N. The gravitational field strength
on the Moon is 1.6 N kg-1.
(1)
Calculate the density of the sample.
Answer:
8125
Explanation:
[tex]P=0,13 N\\a=1,6 N/kg\\m=P/a=0,13/1,6=0,08125\\V=10(cm)^{3} =10^{-5} meters^{3} \\p=m/V=0,08125/10^{-5} =0,08125*100000=8125kg/meters^{3}[/tex]
A stone is thrown vertically downward with an initial speed of 12.0 m/s from the top of a
building. The stone takes 1.54 s to reach the ground.
The question is incomplete; However, the height from which the stone is thrown is most likely to be what's required of the question
Answer:
See Explanation
Explanation:
Given
[tex]Initial\ Speed, u = 12.0m/s[/tex]
[tex]Time, t = 1.54\ s[/tex]
Required
Determine the height
This question will be answered using the following equation of motion;
[tex]S = ut + \frac{1}{2}gt^2[/tex]
Take g as 9.8
This gives:
[tex]S = 12 * 1.54 + \frac{1}{2} * 9.8 * 1.54^2[/tex]
[tex]S = 12 * 1.54 + \frac{1}{2} * 9.8 * 2.3716[/tex]
[tex]S = 18.48 + 11.62084[/tex]
[tex]S = 30.10084[/tex]
[tex]S = 30.1\ m[/tex] (Approximated)
Hence; Height = 30.1m
Juan, a biologist, notices that a particular group of hummingbirds leaves during the colder winter months and returns during the warmer spring months. Juan hypothesizes that the birds fly south to locations with warmer weather and blooming flowers during the winter months. Which procedure should Juan use to test his hypothesis?
Answer:
C. Tag the hummingbirds with transmitters and track their movement.
Explanation:
Hypothesis refers to the conclusion of the analysis found on the grounds of certain observations. The hypothesis is further tested and verified by performing certain experiments. In the given excerpt, Juan hypothesizes that certain group of hummingbirds fly to certain locations depending upon the season. To test the hypothesis, Juan can experiment with finding and tracking the hummingbirds and the direction in which they fly. Tagging the hummingbirds with transmitters and tracking their movement would help Juan concluding about the hypothesis.
Answer:
Tag the hummingbirds with transmitters and track their movement
Explanation:
Suppose a radio signal (light) travels from Earth and through space at a speed of 3 × 108/ (this is the speed of light in vacuum). How far (in meters) into space did the signal travel during the first 10 minutes?
Answer:
18*10^10 meters
Explanation:
V= d/t 10 mins = 600 seconds
3*10^8 = d/600s
(3*10^8)*(6*10^2) = d
d = 18*10^10 m
An object, initially at rest, moves 250 m in 17 s. What is its acceleration?
Answer:
1.73 m/s²
Explanation:
Given:
Δx = 250 m
v₀ = 0 m/s
t = 17 s
Find: a
Δx = v₀ t + ½ at²
250 m = (0 m/s) (17 s) + ½ a (17 s)²
a = 1.73 m/s²
The acceleration of this object is 1.730 meter per seconds square.
Given the following data:
Initial velocity = 2.5 m/s (since the object is starting from rest).Time = 17 seconds.To find the acceleration of this object, we would use the second equation of motion.
Mathematically, the second equation of motion is given by the formula;
[tex]S = ut + \frac{1}{2} at^2[/tex]
Where:
S is the displacement or distance covered.u is the initial velocity.a is the acceleration.t is the time measured in seconds.Substituting the given values into the formula, we have;
[tex]250 = 0(17) + \frac{1}{2} (a)(17^2)\\\\250 = \frac{1}{2} (289)a\\\\250 = 144.5a\\\\a = \frac{250}{144.5}[/tex]
Acceleration, a = 1.730 [tex]m/s^2[/tex]
Therefore, the acceleration of this object is 1.730 meter per seconds square.
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What is the speed of an ocean wave if it’s wavelength is 5.0 m and it’s frequency is 3/s?
Answer:
15 m/s
Explanation:
We know that [tex]v = f * d[/tex] where f = frequency & d = wavelength .
So here.
Wavelength = 5 m
Frequency = 3 s⁻¹
Hence Speed = 5 * 3 = 15 m/s
What exerts the thrust force acting on the cart?
Answer:
This question appears incomplete
Explanation:
The question appears incomplete. However, a thrust can be described as a force or a push. A cart can be described as a vehicle (usually with two wheels) that is used to transport load from one point/place to another.
Newton first law of motion (law of inertia) states that a body will continue to be in a state of rest or if in motion, remains in motion (at constant velocity) unless acted upon by an external force. Hence, a cart will continue to be in a state of rest unless acted on by an external force which can be exerted by animals or humans (depending on the type of cart).
Which of the following statements about slope is NOT true?
Explanation:
did you upload a picture?
The speed of x-rays is 300 000. m/s. In scientific notation, and with the correct number of significant figures, this speed is… *
Answer:
3.0 x 10 and the exponent on ten is 5.
Explanation:
You are moving the decimal point over to the left 5 times, making the exponent a positive 5 and then you would put a decimal after 3. Making it 3.0 x 10, and the exponent 5.
The speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.
The given parameters;
speed of the x-ray, v = 300,000 m/s
The standard form of the given number represents the scientific notation of the number.
To represent a number in standard form, multiply the number in terms of power or exponent of 10. The value of the exponent represents the number of available zeros present.In scientific notation the speed of the x-ray can be expressed as follows;
300,000 m/s = 3.0 x 10⁶ m/s
Thus, the speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.
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If you walk 5 km north and then 12 km east. Your resultant displacement is____.a. magnitude: 1.1km; direction: 53.1 degrees east of north.b. magnitude: 2.00; direction: 53.1 degrees east of north.c. magnitude: 2.00; direction: 36.9 degrees east of north.d. magnitude: 1.1km; direction: 36.9 degrees east of north.
Answer:
Resultant = 13km
Direction = 67.38° East of North
Explanation:
Given the following :
5km North ; 12km East
Resultant Displacement (r) :
r² = 5² + 12²
r² = 25 + 144
r² = 169
r = √169
r = 13
Direction:
Tangent = opposite / Adjacent
Tanθ = opposite / Adjacent
Opposite = 12 ; adjacent = 5
Tanθ = (12/5)
Tanθ = 2.4
θ = tan^-1(2.4)
θ = 67.38° east of north
Three different groups each measured the diameter of a CD three times (the actual diameter of a CD is 12.00cm). The class data is shown in the table. Which group(s) was the most accurate in their measurements? Group 1 only Group 1 only Group 2 only Group 2 only Group 3 only Group 3 only Groups 1 & 3 were equally accurate
If you push a book 1.5 m across a table using a constant force of 10.0 N, how much work do you
do on the book?
Answer:
The answer is
15.0 JExplanation:
To calculate the work done by a body we use the formula
work done = force × distanceFrom the question
force = 10 N
distance covered = 1.5 m
So the work done is
work done = 10 × 1.5
We have the final answer as
15.0 JHope this helps you
Two cylindrical resistors are made from the same material. The shorter one has a length LL and diameter DD . The longer one has a length 16L16L and diameter 4D4D . How do their resistances compare? The resistance of the longer resistor is four times the resistance of the shorter resistor. The resistance of the longer resistor is twice the resistance of the shorter resistor. The resistance of the longer resistor is the same as the resistance of the shorter resistor. The resistance of the longer resistor is half the resistance of the shorter resistor. The resistance of the longer resistor is a quarter of the resistance of the shorter resistor.
Answer:
The resistance of the longer resistor is a quarter of the resistance of the shorter resistor.Explanation:
If Two cylindrical resistors are made from the same material, then their resistivity will be the same. Formula for calculating resistivity of a material is expressed as;
[tex]\rho = \frac{RA}{L} \ where \ A = \frac{\pi d^2}{4}[/tex] where;
R is the resistance
A is the cross sectional area of the material
L is the length of the material
For the shorter cylinder:
Length = L
diameter = D
[tex]\rho = \dfrac{R_s(\frac{\pi D^2}{4})}{L} \\\\\rho = \dfrac{R_s{\pi D^2}}{4L}[/tex]
For the longer cylinder:
Length = 16L
diameter = 4D
[tex]\rho = \dfrac{R_l(\frac{\pi (4D)^2}{4})}{16L} \\\\\\\rho = \dfrac{R_l(\frac{\pi (16D^2)}{4})}{16L} \\\\\rho = \dfrac{R_l{16\pi D^2}}{16L}\\\\\rho = \dfrac{R_l{\pi D^2}}{L}[/tex]
Since their resistivity are the same then;
[tex]\dfrac{R_s{\pi D^2}}{4L} = \dfrac{R_l{\pi D^2}}{L} \\\\ \dfrac{R_s}{4} = {R_l} \\\\R_s = 4R_l\\\\R_l = \frac{R_s}{4}[/tex]
Hence the resistance of the longer resistor is a quarter of the shorter resistor.
A driver looks down at their speedometer and sees they are moving at 45 mph. This measurement would be a
Answer:
This measurement would be a measure of the speed of an object(the car ) in motion
Explanation:
A driver looks down at their speedometer and sees they are moving at 45 mph. This measurement would be about the speed of the car or about how fast the car is moving.
This means, the car is travelling the distance of 45 miles in every hour.
This measurement would also be about the instantenous speed of the car which is 45mph.
Which phrase describes a scientific law?
A. A statement that matter cannot be created or destroyed
B. A claim that experiments cannot verify whether matter has been
destroyed
O C. An explanation for why matter cannot be created or destroyed
D. A prediction of how much matter exists in the universe
SUBMIT
In
Answer:
C- An explanation for why matter cannot be created or destroyed
Explanation:
Answer: A. A statement that matter cannot be created or destroyed.
Explanation:
Apex
Q1. My brakes stop me at -5.5m/s^2 when I lock them up. A puppy runs in front of my car, and I stop just in time 3.5 seconds later. How far did I skid? Q2. I floor the pedal and accelerate from 7.0m/s to 35m/s over a fouth of a mile (0.40km). What is my accelleration?
please explain step by step, much thanks :)
Explanation:
Q1. Given:
v = 0 m/s
a = -5.5 m/s²
t = 3.5 s
Find: Δx
Δx = vt − ½ at²
Δx = (0 m/s) (3.5 s) − ½ (-5.5 m/s²) (3.5 s)²
Δx ≈ 33.7 m
Q2. Given:
Δx = 400 m
v₀ = 7.0 m/s
v = 35 m/s
Find: a
v² = v₀² + 2aΔx
(35 m/s)² = (7.0 m/s)² + 2a (400 m)
a = 1.47 m/s²
A car drives 10km with a speed of 72 km/hr and then runs out of gas. Then you walk 2km for the next 30 min until you find a gas station. (A) What is the displacement of the total trip? (B) How long does the entire trip take? (C) What is the average velocity of the entire trip?
Answer:
A- 12 km
B- 42 minutes
C- 17.14 km per hour
Explanation:
A- The displacement of the total trip is 12 kilometers, which emerges by adding the 10 kilometers traveled by car to the 2 kilometers traveled on foot.
B- The trip, in total, took 42 minutes, which arises from adding the 30 minutes of the journey on foot, plus 12 minutes of travel by car at 72 km / h (72/60 x 10 = 12).
C- While 12 km were covered in 42 minutes, the average speed of the trip was 17.14 km / h. This arises from the following calculation:
42 = 12
60 = X
(60 x 12) / 42 = X
17.14 = X
A ball with mass kg is thrown upward with initial velocity m/s from the roof of a building m high. Neglect air resistance. Use m/s2. Round your answers to one decimal place. (a) Find the maximum height above the ground that the ball reaches. meters (b) Assuming that the ball misses the building on the way down, find the time that it hits the ground. s
Answer:
Explanation:
The question is incomplete. Here is the complete question.
A ball with mass m kg is thrown upward with initial velocity 22 m/s from the roof of a building 17 m high. Neglect air resistance. Use g=9.8 m/s2. Round your answers to one decimal place. (a) Find the maximum height above the ground that the ball reaches. xmax= meters (b) Assuming that the ball misses the building on the way down, find the time that it hits the ground.
a) Using the equation of motion formula;
v² = u²+2gH where;
u is the initial velocity
v is the final velocity
theta is the angle of launch
g is the acceleration due to gravity.
H is the maximum height reached by the ball
Since the ball is thrown upwards, the acceleration due to gravity will be negative. The equation then becomes;
v² = u²-2gH
Given
v = 0m/s
u = 22m/s
g = 9.8m.s²
0² = 22²-2(9.8)H
-22² = -19.6H
H = -22²/-19.6
H = 24.69m
If the biuliding is 17m high, the maximum height above the ground that the ball reaches will be;
Hmax = 24.69+17
Hmax = 41.69m
b) The time it takes to hit the ground can be expressed using the formula
v = u-gt
0 = 22-9.8t
-22 = -9.8t
t = -22/9.8
t = 2.45secs
what are two examples of population distribution?
Which wavelength of light is NOT absorbed by riboflavin?
Answer:
525 nm and 550nm
Explanation:
The absorption spectrum of any compound is a plot of absorption against wavelength. Sometimes, the absorption is plotted against frequency or wave number. This plot appears as humps. The peak of the highest hump is the wavelength of maximum absorption. The concentration of each solution may be indicated above the hump when the instrument is calibrated using different concentrations of the analyte.
The absorption spectrum of riboflavin indicates that its wavelength of maximum absorption is 450nm and it does not absorb at light 525 nm and 550nm wavelengths respectively.
65°F to degrees Celsius
Answer:
18.3 C
Explanation:
Answer: 55/3 °C
Explanation:
Formula:
C=5/9(F-32)
Given:
F=65
Solve:
C=5/9(F-32)
C=5/9(65-32)
C=5/9(33)
C=55/3