Question 1

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 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

The speed of an object is given by 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 4

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 5

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 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 have the same displacement, but opposite velocities. Therefore, their average velocities are equal and zero. Since they are at the same height, they must have the same gravitational potential energy and therefore the same acceleration due to gravity (9.8 m/s^2). Thus, their accelerations are equal but their velocities are equal and opposite.

Question 7

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 8

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 the two children start and end at the same point, their displacement from the origin is zero. However, since Joan is ahead of Mike on the way back, she had to run a greater distance than him to get there. This means that Joan has run a greater distance, but her displacement is less than Mike's.

Question 9

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 motion diagram for D shows that the points are spaced farther apart at later times, indicating an increasing speed. However, the points become closer together again toward the end, indicating a decreasing speed. This means that D speeds up and then slows down. None of the other answer choices are supported by the given diagrams.

Question 10

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 answer of A skier leaves a ski jump with...

Question 11

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 12

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 13

The area under a graph of v_x vs. t from t = t_i to t = t_f represents A) x_i. B) x_f. C) x_f − x_i. D) (x_i + x_f). E) x_i + x_f.

Accepted Answer

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

Question 14

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...

Question 15

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 16

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 17

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 ax_{, avg} so that Δv_x = ax_{, avg}Δt. C) Dallas, because ax_{, avg} 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 18

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. From the information given, we can use the following kinematic equation:

$v_f = v_i + a\Delta t$

where $v_i$ is the initial velocity, $v_f$ is the final velocity, $a$ is the acceleration, and $\Delta t$ is the time interval.

Substituting the given values, we have:

$12.0	ext{ m/s} = 4.0	ext{ m/s} + 4.0	ext{ m/s}^2	imes\Delta t$

Simplifying, we get:

$\Delta t = 2.0	ext{ s}$

Therefore, the displacement of the particle from $t=1.0	ext{ s}$ to $t=3.0	ext{ s}$ is:

$\Delta x = v_i\Delta t + \frac{1}{2}a(\Delta t)^2 = 4.0	ext{ m/s}	imes 2.0	ext{ s} + \frac{1}{2}(4.0	ext{ m/s}^2)	imes(2.0	ext{ s})^2 = 16.0	ext{ m}$

Hence, the area under the position-time graph for the interval from $t=1.0	ext{ s}$ to $t=3.0	ext{ s}$ is 16.0 m$^2$, which is answer choice D.

Question 19

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 20

The area under a graph of a_x vs. t from t = t_i to t = t_f represents A) x_f − x_i. B) v_f − v_i. C) x_avg. D) v_avg. E) a_avg.

Accepted Answer

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

Quiz 2: Motion in One Dimension

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 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?

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

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?

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?

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 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:

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?

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

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 equation that solves a problem is . The problem is:

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

The area under a graph of vx 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

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?

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?

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 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?

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

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

The area under a graph of v_x vs. t from t = t_i to t = t_f represents

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?

The area under a graph of a_x vs. t from t = t_i to t = t_f represents