Question 1

Driver A is cruising along enjoying the fall colors. Driver B starts her car at the instant he passes her. Their velocities are shown as functions of time in the graph below. At what instants in time on the graph are drivers A and B side by side? 
A)0 s, 2 s
B)0 s, 4 s
C)2 s, 4 s
D)2 s, 6 s
E)4 s, 6 s

Accepted Answer

The answer of Driver A is cruising along enjoying the...

Question 2

A particle is moving at constant velocity. Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m. What is the slope of the position-time graph for this particle? A)0, since this is a constant velocity situation. B)4.0 m/s C)4.0 m/s² D)9.0 m/s E)12 m/s²

Accepted Answer

The slope of the position-time graph represents the velocity of the particle. To find the slope (velocity) = (change in position) / (change in time) = (15.0 m - 3.0 m) / (4.0 s - 1.0 s) = 12 m / 3 s = 4.0 m/s.

Question 3

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?
A)Joan has run a greater distance and her displacement is greater than Mike's.
B)Mike has run a greater distance and his displacement is greater than Joan's.
C)Joan has run a greater distance, but her displacement is less than Mike's.
D)Mike has run a greater distance, but his displacement is less than Joan's.
E)Mike has run a shorter distance, and his displacement is less than Joan's.

Accepted Answer

Since Joan is ahead of Mike on the way back, it means that Mike must have crossed the midpoint before Joan did. Therefore, Mike has a greater displacement from the origin compared to Joan. However, since Joan ran ahead of Mike on the way back, she covered a greater distance than Mike. So, Joan has run a greater distance, but her displacement is less than Mike's.

Question 4

A particle is moving with a constant acceleration of 4.0 m/s². Its speed at t = 1.0 s is 4.0 m/s and at t = 3.0 s it is 12.0 m/s. What is the area under the position-time graph for the interval from t = 1.0 s to t = 3.0 s? A)8.0 m/s B)8.0 m C)12 m D)16 m E)16 m/s²

Accepted Answer

The area under the position-time graph represents the displacement of the particle in that time interval. 
Using the formula, 
displacement = initial velocity x time + (1/2) x acceleration x time^2
For the given time interval of 2 seconds, initial velocity u=4.0 m/s, acceleration a=4.0 m/s^2, and time t=2.0 s
Substituting the values, we get
displacement = 4.0 x 2 + (1/2) x 4.0 x 2^2 = 8.0 + 8.0 = 16.0 m
Therefore, the area under the position-time graph for the given time interval is 16.0 m.

Question 5

A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes. Her first lap is toward the north. Her displacement and average velocity are
A)0; 0.
B)0; 2.38 m/s, south.
C)0; 2.38 m/s, north.
D)1 000 m, south; 2.38 m/s, south.
E)1 000 m, north; 2.38 m/s, north.

Accepted Answer

Displacement is a vector quantity that refers to the change in position of an object. Since the swimmer returns to the starting point after completing an even number of laps in a north-south facing pool, the overall change in position is zero, making the displacement 0. Average velocity is displacement divided by time. Since the displacement is 0, the average velocity is also 0, regardless of the distance swum or the time taken.

Question 6

A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point:
A)Their velocities and accelerations are equal.
B)Their velocities are equal but their accelerations are equal and opposite.
C)Their accelerations are equal but their velocities are equal and opposite.
D)Their velocities and accelerations are both equal and opposite.
E)Their velocities are equal to their accelerations.

Accepted Answer

At the halfway point, both balls are changing direction, meaning their velocities are equal and opposite. However, their velocities are different, as one is going up while the other is going down. Therefore, the only possible answer is that their accelerations are equal but their velocities are equal and opposite.

Question 7

In 20 minutes, Kara ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval?
A)0; 0
B)0; 2.00 m/s
C)2.40 km, east; 0
D)2.40 km, east; 2.00 m/s, east
E)2.40 km, west; 2.00 m/s, west

Accepted Answer

The answer of In 20 minutes, Kara ran 2.40 km...

Question 8

The area under a graph of vx vs. t from t = ti to t = tf represents
A)xi.
B)xf.
C)xf − xi.
D)  (xi + xf).
E)xi + xf.

Accepted Answer

The area under a graph of vx vs. t represents the displacement (change in position) of an object. So, the area between ti and tf represents the displacement from xi to xf, which is xf - xi.

Question 9

A skier leaves a ski jump with a horizontal velocity of 29.4 m/s. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are:
A)0; 29.4 m/s.
B)29.4 m/s; 0.
C)29.4 m/s; 29.4 m/s.
D)29.4 m/s; 41.6 m/s.
E)41.6 m/s; 41.6 m/s.

Accepted Answer

The horizontal velocity remains constant throughout the jump, so the horizontal velocity remains 29.4 m/s. The vertical velocity at the top of the jump is 0 m/s (since the skier is momentarily motionless at the top of the arc), and we know that three seconds later the skier lands, so the vertical displacement during those three seconds is the same as the vertical displacement that occurred during the time the skier was in the air. Using the kinematic equation s = ut + ½at² with s = -h (where h is the vertical height of the jump), u = 0 m/s (since the skier starts from rest at the top of the jump), a = -9.8 m/s² (since the only force acting on the skier in the vertical direction is gravity, and it acts downwards), and t = 3 s, we have:

-h = 0 + ½(-9.8)(3)²
-h = -44.1 m

Therefore, the vertical component of the skier's velocity three seconds before landing is:

v = u + at = 0 + (-9.8)(3)
v = -29.4 m/s

The magnitude of this velocity is 29.4 m/s (since speed is the magnitude of velocity), so the best choice is C, with a horizontal velocity of 29.4 m/s and a vertical velocity of 29.4 m/s.

Question 10

The speed of an object is given by v = 5.00t2 +4, where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s? A)5.00 m/s² B)9.00 m/s² C)10.0 m/s² D)14.0 m/s² E)20.0 m/s²

Accepted Answer

The answer of The speed of an object is given...

Question 11

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct?  ​
A)A has the greatest speed and the greatest acceleration.
B)C has decreasing speed.
C)D slows down and then speeds up.
D)D speeds up and then slows down.
E)E has a greater speed than A.

Accepted Answer

The answer of Five motion diagrams in which points represent...

Question 12

A car travels north at 30 m/s for one half hour. It then travels south at 40 m/s for 15 minutes. The total distance the car has traveled and its displacement are:
A)18 km; 18 km S.
B)36 km; 36 km S.
C)36 km; 36 km N.
D)90 km; 18 km N.
E)90 km; 36 km N.

Accepted Answer

The total distance traveled is the sum of the distances in both directions: north (30 m/s * 1800 s = 54,000 m or 54 km) and south (40 m/s * 900 s = 36,000 m or 36 km), which equals 90 km. The displacement is the difference between the distances north and south, which is 54 km - 36 km = 18 km north.

Question 13

Dallas says that any change in velocity is directly proportional to the time interval over which the change took place. Dana says that is true only when the acceleration is constant. Which one, if either, is correct?
A)Dana, because it is true only when the acceleration is constant.
B)Dallas, because we can define  so that Δvx =  Δt.
C)Dallas, because  always is equal to  .
D)All the above are correct.
E)Only (a) and (b) above are correct.

Accepted Answer

The answer of Dallas says that any change in velocity...

Question 14

The equation that solves a problem is  . The problem is:
A)How far above its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground?
B)How far below its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground?
C)What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released?
D)What is the change in position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released?
E)What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground if its maximum height is 33.6 m?

Accepted Answer

The answer of The equation that solves a problem is...

Question 15

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals. Assume the body moves in a straight line.  This diagram is most likely to describe
A)a swimmer swimming laps.
B)an exercise on a rowing machine.
C)a person on a treadmill.
D)a tennis ball during a volley.
E)a runner who tripped, fell, rose, and continued racing.

Accepted Answer

The answer of The small circles in the diagram below...

Question 16

A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the average acceleration of the ball during this time interval?

Accepted Answer

The answer of A 50-gram superball traveling at 25.0 m/s...

Question 17

The equation that solves a problem is . The problem is: A)What is the initial velocity of a car that goes from rest to 18 m/s in 3.0 s? B)What is the final velocity of a car that goes from rest to 18 m/s in 3.0 s? C)What is the initial velocity of a car that accelerates at 18 m/s for 3.0 s? D)What is the final velocity of a car that accelerates at 3.0 m/s² over a 6.0 m distance? E)What is the final velocity of a car that accelerates at 3.0 m/s² over a 3.0 m distance?

Accepted Answer

The answer of The equation that solves a problem is...

Question 18

A boat moves at 10.0 m/s relative to the water. If the boat is in a river where the current is 2.0 m/s, how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

Accepted Answer

The answer of A boat moves at 10.0 m/s relative...

Question 19

The area under a graph of ax vs. t from t = ti to t = tf represents
A)xf − xi.
B)vf − vi.
C)xav.
D)vav.
E)aav.

Accepted Answer

The answer of The area under a graph of ax...

Question 20

A problem may be solved more easily when alternative representations are used. The best strategy is to formulate representations in an order that assists in understanding the physical principles involved. Of the orders given below, the one that will work best most often is
A)pictorial representation, mathematical representation, tabular representation, mental representation.
B)pictorial representation, mental representation, mathematical representation, tabular representation.
C)mathematical representation, pictorial representation, tabular representation, mental representation.
D)mathematical representation, tabular representation, mental representation, pictorial representation.
E)mental representation, pictorial representation, tabular representation, mathematical representation.

Accepted Answer

The answer of A problem may be solved more easily...

Quiz 2: One-Dimensional Motion

Driver A is cruising along enjoying the fall colors. Driver B starts her car at the instant he passes her. Their velocities are shown as functions of time in the graph below. At what instants in time on the graph are drivers A and B side by side?

A particle is moving at constant velocity. Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m. What is the slope of the position-time graph for this particle?

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?

A particle is moving with a constant acceleration of 4.0 m/s2. Its speed at t = 1.0 s is 4.0 m/s and at t = 3.0 s it is 12.0 m/s. What is the area under the position-time graph for the interval from t = 1.0 s to t = 3.0 s?

A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes. Her first lap is toward the north. Her displacement and average velocity are

A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point:

In 20 minutes, Kara ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval?

The area under a graph of vx vs. t from t = ti to t = tf represents

A skier leaves a ski jump with a horizontal velocity of 29.4 m/s. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are:

The speed of an object is given by v = 5.00t2 +4, where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct? ​

A car travels north at 30 m/s for one half hour. It then travels south at 40 m/s for 15 minutes. The total distance the car has traveled and its displacement are:

Dallas says that any change in velocity is directly proportional to the time interval over which the change took place. Dana says that is true only when the acceleration is constant. Which one, if either, is correct?

The equation that solves a problem is . The problem is:

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals. Assume the body moves in a straight line. This diagram is most likely to describe

A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the average acceleration of the ball during this time interval?

The equation that solves a problem is . The problem is:

A boat moves at 10.0 m/s relative to the water. If the boat is in a river where the current is 2.0 m/s, how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

The area under a graph of ax vs. t from t = ti to t = tf represents

A problem may be solved more easily when alternative representations are used. The best strategy is to formulate representations in an order that assists in understanding the physical principles involved. Of the orders given below, the one that will work best most often is

A particle is moving with a constant acceleration of 4.0 m/s². Its speed at t = 1.0 s is 4.0 m/s and at t = 3.0 s it is 12.0 m/s. What is the area under the position-time graph for the interval from t = 1.0 s to t = 3.0 s?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct?