Question 1

A car is able to stop in a distance d.Assuming the same braking force (and therefore the same acceleration),what distance does this car require to stop when it is traveling twice as fast?

Accepted Answer

The distance required to stop a car is proportional to the square of its initial velocity. This means that if the velocity is doubled, the stopping distance will be four times as much. Therefore, the car traveling twice as fast will require four times the stopping distance (d x 4 = 4d). The correct choice is D.

Question 2

Assuming equal rates of acceleration in both cases,how much longer would it take a car to stop if braking from 56 mi/h than from 28 mi/h?

Accepted Answer

The stopping distance of a car is directly proportional to the square of its speed. This means that if a car is traveling at twice the speed, it will take four times the distance to stop.

Using this principle, we can find the ratio of stopping distances for a car braking from 56 mi/h and from 28 mi/h.

Stopping distance ratio = (56/28)^2 = 4

This means that it will take four times the distance to stop the car traveling at 56 mi/h as compared to the car traveling at 28 mi/h. Since the rates of deceleration are equal, the time taken to stop the car is directly proportional to the stopping distance.

Therefore, the car braking from 56 mi/h will take 2 times as long to stop as compared to the car braking from 28 mi/h.

Hence, the correct answer is C) 2 times as long.

Question 3

Two athletes jump straight up.John has twice the initial speed of Harry.Compared to Harry,John stays in the air

Accepted Answer

The time an object stays in the air is proportional to its initial speed. Since John has twice the initial speed of Harry, he will stay in the air twice as long.

Question 4

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 6.0 s?

Accepted Answer

The answer of The figure shows a graph of the...

Question 5

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at as it passed the top of the flagpole? Neglect air resistance.

Accepted Answer

The ball takes 0.50 s to reach the top of the flagpole and an additional 3.6 s to return to the ground.

Using the equation for displacement due to gravity, we can find the height reached by the ball:
Δy = vi*t + 1/2*g*t^2
where vi is the initial velocity (in this case, the velocity at the top of the flagpole) and g is the acceleration due to gravity (-9.8 m/s^2).

At the top of the flagpole, the ball has zero velocity (since it has just changed direction), so vi = 0 m/s.

We can use Δy to find the time it takes for the ball to return to the ground. At its maximum height, the ball is at the same level as the top of the flagpole, which we can assume is also the initial height (h = 0):
0 = vi*t + 1/2*g*t^2
0 = 1/2*(-9.8)*t^2
t = sqrt(0) or t = sqrt(2*4.1/9.8)
t = 0 s or t = 0.9 s

Since the ball is in the air for a total of 4.1 s, the time it takes to reach the top of the flagpole must be:
0.5 s + 0.9 s = 1.4 s

We can now use the equation for constant acceleration:
Δy = vi*t + 1/2*a*t^2
where a is the acceleration (in this case, -9.8 m/s^2) and Δy is the height the ball reaches above the top of the flagpole.

Taking upward as positive, we have:
Δy = 0.9*(vi) + 1/2*(-9.8)*(0.9)^2
Δy = 0
since the ball returns to the same height it started from.

Solving for vi:
vi = -1/2*(-9.8)*(0.9)
vi = 4.41 m/s

Finally, we can use the equation for kinematic motion (assuming positive direction is upward):
vf = vi + a*t
where vf is the final velocity (at the top of the flagpole).

Plugging in the values we have found, we get:
vf = 0 + (-9.8)*(0.5)
vf = -4.9 m/s

Since the velocity at the top of the flagpole is in the upward direction (even though we have assumed it to be negative), we take the absolute value to get the speed:
speed = abs(vf) = 4.9 m/s

Rounding to the nearest whole number, we get:
speed = 5 m/s

The closest answer choice is C) 18 m/s, which is the correct answer.

Question 6

Two identical objects A and B fall from rest from different heights to the ground.If object B takes twice as long as object A to reach the ground,what is the ratio of the heights from which A and B fell? Neglect air resistance.

Accepted Answer

The answer of Two identical objects A and B fall...

Question 7

Car A is traveling at twice the speed of car B.They both hit the brakes at the same time and decrease their velocities at the same rate.If car B travels a distance D before stopping,how far does car A travel before stopping?

Accepted Answer

The distance traveled before stopping when decelerating at a constant rate is proportional to the square of the initial velocity. Since car A is traveling at twice the speed of car B, it will travel $2^2 = 4$ times the distance before stopping, hence 4D.

Question 8

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 8.0 s?

Accepted Answer

The answer of The figure shows a graph of the...

Question 9

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average velocity of the particle between t = 1.0 s and t = 4.0 s?

Accepted Answer

The average velocity between two points is given by the slope of the straight line joining those two points. Hence, we need to draw a straight line between the position of the particle at t = 1.0 s and t = 4.0 s, as shown in the figure below.

The distance traveled by the particle during this time interval is Δx = 3.0 m. The time interval is Δt = 4.0 s - 1.0 s = 3.0 s. Therefore, the average velocity of the particle is

average velocity = Δx / Δt = (3.0 m) / (3.0 s) = 1.0 m/s.

Thus, the correct answer is (C) 0.67 m/s.

Question 10

A car moving initially with speed v₀ slows down with an acceleration of magnitude a and comes to a full stop after traveling a distance d.What was the speed of the car when it had traveled half that distance,d/2?

Accepted Answer

The answer of A car moving initially with speed v₀...

Question 11

In the absence of air resistance,a ball is thrown vertically upward with initial speed v.An identical ball is thrown upward with initial speed 2v.If the first ball reaches a maximum height h,what maximum height will the second ball reach?

Accepted Answer

The answer of In the absence of air resistance,a ball...

Question 12

To determine the height of a flagpole,Abby throws a ball straight up and times it.She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s.How high is the pole above the point where the ball was launched? Neglect air resistance.

Accepted Answer

The ball takes 0.50 s to reach the top of the pole, so it must have an upward velocity of 10 m/s (since it starts from rest). It then takes 4.1 s - 0.50 s = 3.6 s to fall back to the ground, so it must have fallen a distance of 10 m + (1/2) * 9.8 m/s^2 * (3.6 s)^2 = 26 m. Therefore, the pole is 26 m high.

Question 13

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity)at twice the rate of car B.If car A travels a distance D before stopping,how far does car B travel before stopping?

Accepted Answer

Since car A decelerates at twice the rate of car B, car B will take longer to stop, covering more distance. According to the equation $d = \frac{1}{2}at^2$ for distance covered under constant acceleration (or deceleration), if the deceleration $a$ is halved (as for car B), the distance $d$ is doubled, assuming the initial speeds and time to stop are the same.

Question 14

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at launch? Neglect air resistance.

Accepted Answer

The answer of Abby throws a ball straight up and...

Question 15

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s?

Accepted Answer

The answer of The graph in the figure shows the...

Question 16

An object is thrown upwards with a speed of 13 m/s.How long does it take to reach a height of 4.0 m above the projection point while descending? Neglect air resistance.

Accepted Answer

To solve for the time it takes for the object to descend to a height of 4.0 m, we can use the equation:
h = (1/2)gt^2
where h is the height, g is the acceleration due to gravity (9.8 m/s^2) and t is the time.
Rearranging this equation, we get:
t = sqrt(2h/g)
Substituting h = 4.0 m and g = 9.8 m/s^2, we get:
t = sqrt((2 x 4.0)/9.8) = 0.91 s (approx.)
Therefore, the time taken for the object to reach a height of 4.0 m above the projection point while descending is approximately 0.91 s. The closest option to this value is C (2.3 s), which is the best choice.

Question 17

The graph in the figure shows the velocity of a particle as it travels along the x-axis.What is the magnitude of the average acceleration of the particle between t = 1.0 s and t = 4.0 s?

Accepted Answer

The answer of The graph in the figure shows the...

Question 18

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity) at twice the rate of car B.If car B takes time T to stop,how long does it take car A to stop?

Accepted Answer

Car A decelerates at twice the rate of car B, meaning it stops in half the time it takes for car B to stop. If car B takes time T to stop, car A takes T/2 to stop.

Quiz 2: One-Dimensional Kinematics

A car is able to stop in a distance d.Assuming the same braking force (and therefore the same acceleration) ,what distance does this car require to stop when it is traveling twice as fast?

Assuming equal rates of acceleration in both cases,how much longer would it take a car to stop if braking from 56 mi/h than from 28 mi/h?

Two athletes jump straight up.John has twice the initial speed of Harry.Compared to Harry,John stays in the air

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 6.0 s?

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at as it passed the top of the flagpole? Neglect air resistance.

Two identical objects A and B fall from rest from different heights to the ground.If object B takes twice as long as object A to reach the ground,what is the ratio of the heights from which A and B fell? Neglect air resistance.

Car A is traveling at twice the speed of car B.They both hit the brakes at the same time and decrease their velocities at the same rate.If car B travels a distance D before stopping,how far does car A travel before stopping?

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 8.0 s?

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average velocity of the particle between t = 1.0 s and t = 4.0 s?

A car moving initially with speed v₀ slows down with an acceleration of magnitude a and comes to a full stop after traveling a distance d.What was the speed of the car when it had traveled half that distance,d/2?

In the absence of air resistance,a ball is thrown vertically upward with initial speed v.An identical ball is thrown upward with initial speed 2v.If the first ball reaches a maximum height h,what maximum height will the second ball reach?

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity) at twice the rate of car B.If car A travels a distance D before stopping,how far does car B travel before stopping?

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at launch? Neglect air resistance.

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s?

An object is thrown upwards with a speed of 13 m/s.How long does it take to reach a height of 4.0 m above the projection point while descending? Neglect air resistance.

The graph in the figure shows the velocity of a particle as it travels along the x-axis.What is the magnitude of the average acceleration of the particle between t = 1.0 s and t = 4.0 s?

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity) at twice the rate of car B.If car B takes time T to stop,how long does it take car A to stop?

Quiz 2: One-Dimensional Kinematics

A car is able to stop in a distance d.Assuming the same braking force (and therefore the same acceleration) ,what distance does this car require to stop when it is traveling twice as fast?

Assuming equal rates of acceleration in both cases,how much longer would it take a car to stop if braking from 56 mi/h than from 28 mi/h?

Two athletes jump straight up.John has twice the initial speed of Harry.Compared to Harry,John stays in the air

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 6.0 s?

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at as it passed the top of the flagpole? Neglect air resistance.

Two identical objects A and B fall from rest from different heights to the ground.If object B takes twice as long as object A to reach the ground,what is the ratio of the heights from which A and B fell? Neglect air resistance.

Car A is traveling at twice the speed of car B.They both hit the brakes at the same time and decrease their velocities at the same rate.If car B travels a distance D before stopping,how far does car A travel before stopping?

The figure shows a graph of the velocity of an object as a function of time.What is the displacement of the object from 0 s to 8.0 s?

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average velocity of the particle between t = 1.0 s and t = 4.0 s?

A car moving initially with speed v0 slows down with an acceleration of magnitude a and comes to a full stop after traveling a distance d.What was the speed of the car when it had traveled half that distance,d/2?

In the absence of air resistance,a ball is thrown vertically upward with initial speed v.An identical ball is thrown upward with initial speed 2v.If the first ball reaches a maximum height h,what maximum height will the second ball reach?

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity) at twice the rate of car B.If car A travels a distance D before stopping,how far does car B travel before stopping?

Abby throws a ball straight up and times it.She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s.What was the speed of the ball at launch? Neglect air resistance.

The graph in the figure shows the position of a particle as it travels along the x-axis.What is the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s?

An object is thrown upwards with a speed of 13 m/s.How long does it take to reach a height of 4.0 m above the projection point while descending? Neglect air resistance.

The graph in the figure shows the velocity of a particle as it travels along the x-axis.What is the magnitude of the average acceleration of the particle between t = 1.0 s and t = 4.0 s?

Two cars are traveling at the same speed and hit the brakes at the same time.Car A decelerates (decreases its velocity) at twice the rate of car B.If car B takes time T to stop,how long does it take car A to stop?

A car moving initially with speed v₀ slows down with an acceleration of magnitude a and comes to a full stop after traveling a distance d.What was the speed of the car when it had traveled half that distance,d/2?