Question 1

A strobe photograph shows equally-spaced images of a car moving along a straight road.If the time intervals between images is constant,which of the following cannot be positive?
A)the speed of the car
B)the average velocity of the car
C)the acceleration of the car
D)the direction of motion of the car

Accepted Answer

If the images are equally spaced, it indicates that the car is moving at a constant speed, meaning the acceleration is zero, not positive.

Question 2

Starting from rest,a car accelerates down a straight road with constant acceleration a for a time t,then the direction of the acceleration is reversed, (i.e. ,it is −a),and the car comes to a stop in an additional time t,the time for the whole trip being 2t.At what time,or times,is the average velocity of the car for the trip equal to its instantaneous velocity during the trip?
A)There is no such time.
B)It is at the halfway point at t.
C)This occurs at 2 times,0.5t and 1.5t.
D)This occurs at 2 times,0.707t and 1.293t.

Accepted Answer

The average velocity of the car for the trip is equal to its instantaneous velocity at the points where the car has covered half of the total distance in each segment of the trip, which occurs at 0.5t and 1.5t.

Question 3

An object moves at a constant velocity of 12 m/s to the southwest for an interval of 20 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?
A)It can be any value from 0 to 24 m/s.
B)6 m/s
C)12 m/s
D)More information is needed.

Accepted Answer

Since the object is moving at a constant velocity, its velocity does not change. Therefore, its instantaneous velocity at any point during the 20 s interval is still 12 m/s, including halfway through the interval.

Question 4

If a is acceleration,v is velocity,x is position,and t is time,then which equation is not dimensionally correct? A)t = x/v B)a = v²/x C)v = a/t D)t² = 2x/a

Accepted Answer

The answer of If a is acceleration,v is velocity,x is...

Question 5

The slope of the acceleration vs.time curve represents
A)the velocity.
B)the rate of change of acceleration.
C)the rate of change of displacement.
D)the area under the position vs.time curve.

Accepted Answer

The slope of the acceleration vs. time curve represents the rate of change of acceleration. This is because acceleration is the rate of change of velocity, and the slope of the acceleration vs. time curve represents how quickly the acceleration is changing over time. Option A is incorrect because velocity is represented by the slope of the position vs. time curve, not the acceleration vs. time curve. Option C is incorrect because the rate of change of displacement is represented by the slope of the velocity vs. time curve, not the acceleration vs. time curve. Option D is incorrect because the area under the position vs. time curve represents displacement, not acceleration.

Question 6

​Suppose a particle is moving along a straight line with a speed v for a time t,then stops for a time t,and then resumes moving along the original direction with speed v for time t.What has been the average speed of the particle for the total time period 3t?
A)v
B) 
C)1.5v
D)

Accepted Answer

The answer of ​Suppose a particle is moving along a...

Question 7

On a velocity-time graph for a particle,suppose the plot starts at some positive velocity and then follows a straight line to zero at a later time.Which of the following must be true about a position vs.time graph for this same time interval?
A)The curve will start at a positive position value and follow a straight line to zero at the later time.
B)The curve will rise steeply at first and as time goes on will level out approaching its highest position value at the later time.
C)The curve will drop steeply at first and as time goes on will approach its lowest position value at the later time
D)The curve will start at the zero of position and follow a straight line to its highest position at the later time.

Accepted Answer

Since the velocity is decreasing uniformly with time, it indicates that the particle is slowing down at a constant rate. This means that the particle is decelerating, and thus the acceleration is negative. Using the kinematic equations, we know that for a particle with constant negative acceleration, the position-time graph is a downward-facing parabola. Therefore, the curve will rise steeply at first (due to positive initial velocity) and as time goes on will level out approaching its highest position value (at the vertex of the parabola) at the later time.

Question 8

A v vs.t graph is drawn for a ball moving in one direction.The graph starts at the origin and at t = 5 s the acceleration of the ball is zero.We know that at t = 5 s,
A)the slope of the curve is non-zero.
B)the velocity of the ball is not changing.
C)the curve is not crossing the time axis.
D)the curve is at v = 0,t = 0.

Accepted Answer

At t=5 s, the acceleration is zero, which means the velocity is constant. Therefore, the slope of the curve (which represents the acceleration) is zero, and the velocity is not changing. So, the correct choice is B. The other choices are not necessarily true. For example, the curve might cross the time axis or have a non-zero slope at t=5 s. Also, we do not know if the curve is at v=0, t=0, as there is no information given about the initial velocity of the ball.

Question 9

A rock is rolled in the sand.It starts at 5.0 m/s,moves in a straight line for a distance of 6.0 m,and then stops.What is the magnitude of the average acceleration? A)2.1 m/s² B)4.2 m/s² C)5.4 m/s² D)6.2 m/s²

Accepted Answer

The magnitude of the average acceleration can be calculated using the formula $a = \frac{v^2 - u^2}{2s}$, where $v$ is the final velocity (0 m/s, since it stops), $u$ is the initial velocity (5.0 m/s), and $s$ is the distance (6.0 m). Plugging in the values, we get $a = \frac{0^2 - 5.0^2}{2 \times 6.0} = \frac{-25}{12} = -2.1$ m/s$^2$. The negative sign indicates the direction of acceleration is opposite to the direction of motion, but since the question asks for magnitude, we take the absolute value, which is 2.1 m/s$^2$.

Question 10

In which of the following cases is the displacement's magnitude half the distance traveled?​
A)10 steps east followed by 3 steps west
B)28 steps east followed by 14 steps west
C)6 steps east followed by 24 steps west
D)12 steps east followed by 4 steps west
E)​5 steps east followed by 25 steps west

Accepted Answer

The answer of In which of the following cases is...

Question 11

A car is moving along a straight highway and accelerates at a constant rate while going from point A to point B.If the acceleration is positive,increasing the speed of the car,where does the position where the instantaneous speed equals the average speed occur for the interval from A to B?
A)midway between A and B
B)closer to A than to B
C)closer to B than to A
D)Any of the answers could be correct depending on the original speed.

Accepted Answer

The answer of A car is moving along a straight...

Question 12

On a position-time graph for a particle,suppose the plot starts at some positive position and as the time goes on the curve gets steeper and steeper while curving upwards.Which of the following must be true?
A)The speed of the particle is constant.
B)The acceleration of the particle is constant.
C)The speed of the particle is decreasing.
D)The acceleration of the particle is positive.

Accepted Answer

If the curve is getting steeper and curving upwards, it means that the slope of the curve (which represents velocity) is increasing. Therefore, the particle is accelerating, and since the curve is curving upwards, the acceleration must be positive. Choice A and C can be ruled out because the slope of the curve is not constant, and so the speed of the particle cannot be constant or decreasing.

Question 13

Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration,x is distance,and t is time) A)v/t² B)vx² C)v²/t D)at

Accepted Answer

Velocity has the dimension of distance divided by time (L/T). Option D, at, where a is acceleration (L/T^2) and t is time (T), gives the dimension L/T^2 * T = L/T, which is the dimension of velocity.

Question 14

An object moves along the x axis,with its position given by the function x(t)= ½ t³.Which of the following can be obtained from a graph of x vs.t? A)The velocity of the object at any instant in time B)The displacement of the object during a specified time interval C)The speed of the particle at any instant in time D)The average velocity of the object during as specified time interval E)All of the above

Accepted Answer

A graph of x vs. t is a position vs. time graph, and from this graph, we can obtain all of the listed quantities. 
Velocity is given by the slope of the tangent line to the position vs. time graph at any given point, so we can determine the velocity at any instant in time from the graph. 
Displacement is the change in position over a specified time interval, which can be found by calculating the area under the velocity vs. time graph within that time interval. 
Speed is the absolute value of velocity, so we can obtain this from the same tangent lines used to find velocity. 
Average velocity can be found by calculating the slope of the line connecting two points on the position vs. time graph, representing the object's average displacement over a specified time interval. Therefore, all of the listed options can be obtained from a graph of x vs. t.

Question 15

A 50.0-g ball traveling at 22.0 m/s is bounced off a brick wall and rebounds at 21.0 m/s.A high-speed camera records this event.If the ball is in contact with the wall for 2.50 ms,what is the average acceleration of the ball during this time interval? A)1.72E+4 m/s² B)3.44E+4 m/s² C)8.60E+3 m/s² D)1.72E+1 m/s² E)4.30E+1 m/s²

Accepted Answer

The average acceleration can be calculated using the formula: a = (v_f - v_i) / Δt. Here, v_i = 22.0 m/s, v_f = -21.0 m/s (since it rebounds in the opposite direction), and Δt = 2.50 ms = 0.0025 s. Thus, a = (-21.0 - 22.0) / 0.0025 = -43.0 / 0.0025 = -1.72E+4 m/s².

Question 16

A strobe photograph of a car moving along a straight road shows the interval between each successive image to be diminishing.If the direction of motion of the car is taken as positive,which of the following is/are negative?
A)the speed of the car
B)the average velocity of the car
C)the average acceleration of the car
D)all of the above

Accepted Answer

The diminishing interval between each successive image indicates that the car is decelerating. If the direction of motion is positive, a deceleration (or negative acceleration) means the car is slowing down, hence the average acceleration is negative. Speed, being a scalar, cannot be negative, and the average velocity, which is direction-dependent, is positive since the car continues to move in the positive direction despite slowing down.

Question 17

A ball is pushed downhill with an initial velocity of 3.0 m/s.The ball rolls down a hill with a constant acceleration of 1.6 m/s².The ball reaches the bottom of the hill in 6.0 s.What is the ball's velocity at the bottom of the hill? A)10 m/s B)13 m/s C)16 m/s D)17 m/s

Accepted Answer

The ball's velocity at the bottom of the hill can be calculated using the formula $v = u + at$, where $v$ is the final velocity, $u$ is the initial velocity (3.0 m/s), $a$ is the acceleration (1.6 m/s$^2$), and $t$ is the time (6.0 s). Plugging in the values, we get $v = 3.0 m/s + (1.6 m/s^2 \times 6.0 s) = 3.0 m/s + 9.6 m/s = 12.6 m/s$, which rounds to 13 m/s.

Question 18

An x vs.t graph is drawn for a ball moving in one direction.The graph starts at the origin and at t = 5 s the velocity of the ball is zero.We can be positive that at t = 5 s,
A)the slope of the curve is non-zero.
B)the ball has stopped.
C)the acceleration is constant.
D)the curve is at x = 0,t = 0.

Accepted Answer

At t=5s, the velocity of the ball is zero which means the ball has stopped. This is indicated by the intersection of the x-axis and the graph. The slope of the curve is zero at this point. The acceleration may or may not be constant, and the curve could be at any value of x as it depends on the initial conditions of the motion.

Question 19

The value of an object's acceleration may be characterized in equivalent words by which of the following?
A)displacement
B)rate of change of displacement
C)velocity
D)rate of change of velocity

Accepted Answer

Acceleration is defined as the rate of change of velocity. Therefore, the equivalent words to describe acceleration are the rate of change of velocity. Displacement and velocity are not directly related to acceleration.

Question 20

A car is moving in the positive direction along a straight highway and accelerates at a constant rate while going from point A to point B.If the acceleration is positive,increasing the speed of the car,when does the position where the average speed equals the instantaneous speed occur during the time interval from A to B? Assume the time interval is T.
A)T/2 from the start of the interval
B)before T/2 from the start of the interval
C)after T/2 from the start of the interval
D)It depends on the speed at the start of the time interval.

Accepted Answer

The position where the average speed equals the instantaneous speed occurs at T/2 from the start of the interval due to the symmetry of the motion under constant acceleration.

Quiz 2: Motion in One Dimension

A strobe photograph shows equally-spaced images of a car moving along a straight road.If the time intervals between images is constant,which of the following cannot be positive?

An object moves at a constant velocity of 12 m/s to the southwest for an interval of 20 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?

If a is acceleration,v is velocity,x is position,and t is time,then which equation is not dimensionally correct?

The slope of the acceleration vs.time curve represents

Suppose a particle is moving along a straight line with a speed v for a time t,then stops for a time t,and then resumes moving along the original direction with speed v for time t.What has been the average speed of the particle for the total time period 3t?

On a velocity-time graph for a particle,suppose the plot starts at some positive velocity and then follows a straight line to zero at a later time.Which of the following must be true about a position vs.time graph for this same time interval?

A v vs.t graph is drawn for a ball moving in one direction.The graph starts at the origin and at t = 5 s the acceleration of the ball is zero.We know that at t = 5 s,

A rock is rolled in the sand.It starts at 5.0 m/s,moves in a straight line for a distance of 6.0 m,and then stops.What is the magnitude of the average acceleration?

In which of the following cases is the displacement's magnitude half the distance traveled?

A car is moving along a straight highway and accelerates at a constant rate while going from point A to point B.If the acceleration is positive,increasing the speed of the car,where does the position where the instantaneous speed equals the average speed occur for the interval from A to B?

On a position-time graph for a particle,suppose the plot starts at some positive position and as the time goes on the curve gets steeper and steeper while curving upwards.Which of the following must be true?

Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration,x is distance,and t is time)

An object moves along the x axis,with its position given by the function x(t) = ½ t³.Which of the following can be obtained from a graph of x vs.t?

A 50.0-g ball traveling at 22.0 m/s is bounced off a brick wall and rebounds at 21.0 m/s.A high-speed camera records this event.If the ball is in contact with the wall for 2.50 ms,what is the average acceleration of the ball during this time interval?

A strobe photograph of a car moving along a straight road shows the interval between each successive image to be diminishing.If the direction of motion of the car is taken as positive,which of the following is/are negative?

A ball is pushed downhill with an initial velocity of 3.0 m/s.The ball rolls down a hill with a constant acceleration of 1.6 m/s².The ball reaches the bottom of the hill in 6.0 s.What is the ball's velocity at the bottom of the hill?

An x vs.t graph is drawn for a ball moving in one direction.The graph starts at the origin and at t = 5 s the velocity of the ball is zero.We can be positive that at t = 5 s,

The value of an object's acceleration may be characterized in equivalent words by which of the following?