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?

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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?

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?

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?

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

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:

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?

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Question 8

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

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:

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?

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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?  ​

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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:

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?

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

Question 14

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

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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

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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?

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Question 17

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

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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?

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Question 19

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

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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

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

Quiz 2: One-Dimensional Motion