Accelerated Motion Quiz

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Questions and Answers

The velocity-time graph in Figure 8 describes Steven's motion as he walks along the midway at the state fair. Sketch the corresponding motion diagram. Include velocity vectors in your diagram.

To answer this question, you will need to refer to Figure 8 in the text. The motion diagram will depict Steven's position at various time intervals with arrows representing his velocity at each point, showing changes in velocity over time.

Use the v-t graph of the toy train in Figure 9 to answer these questions: When is the train's speed constant?

15.0 to 20.0 s

0.0 to 5.0 s

20.0 to 25.0 s

5.0 to 15.0 s (correct)

Use the v-t graph of the toy train in Figure 9 to answer these questions: During which time interval is the train's acceleration positive?

0.0 to 5.0 s (correct)

5.0 to 15.0 s

20.0 to 25.0 s

15.0 to 20.0 s

Use the v-t graph of the toy train in Figure 9 to answer these questions: When is the train's acceleration most negative?

15.0 to 20.0 s Signup and view all the answers

Refer to Figure 9 to find the average acceleration of the train during the following time intervals: 0.0 s to 5.0 s

2.0 m/s^2 Signup and view all the answers

A race car's forward velocity increases from 4.0 m/s to 36 m/s over a 4.0-s time interval. What is its average acceleration?

8.0 m/s^2 forward Signup and view all the answers

The race car in the previous problem slows from 36 m/s to 15 m/s over 3.0 s. What is its average acceleration?

7.0 m/s^2 backward Signup and view all the answers

A bus is moving west at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. What is the average acceleration of the bus while braking?

8.3 m/s^2 east Signup and view all the answers

A bus is moving west at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. If the bus took twice as long to stop, how would the acceleration compare with what you found in part a?

Half as great Signup and view all the answers

A car is coasting backward downhill at a speed of 3.0 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.5 m/s. If uphill is chosen as the positive direction, what is the car's average acceleration?

3.0 m/s^2 Signup and view all the answers

Rohith has been jogging east toward the bus stop at 3.5 m/s when he looks at his watch and sees that he has plenty of time before the bus arrives. Over the next 10.0 s, he slows his pace to a leisurely 0.75 m/s. What was his average acceleration during this 10.0 s?

0.28 m/s^2 west Signup and view all the answers

If the rate of continental drift were to abruptly slow from 1.0 cm/y to 0.5 cm/y over the time interval of a year, what would be the average acceleration?

0.5 cm/yr^2 in the direction opposite the drift Signup and view all the answers

What are three ways an object can accelerate?

all of the above Signup and view all the answers

Two joggers run at a constant velocity of 7.5 m/s east. Figure 10 shows the positions of both joggers at time t = 0. What would be the difference(s) in the position-time graphs of their motion?

Both lines would have the same slope, but they would have different y-intercepts. Signup and view all the answers

Two joggers run at a constant velocity of 7.5 m/s east. Figure 10 shows the positions of both joggers at time t = 0. What would be the difference(s) in their velocity-time graphs?

Their velocity-time graphs would be identical Signup and view all the answers

Sketch a velocity-time graph for a car that goes east at 25 m/s for 100 s, then west at 25 m/s for another 100 s.

The graph should have two horizontal line segments. The first segment should be above the horizontal axis and extend from 0 s to 100 s, representing the car's constant eastward velocity. The second segment should be below the horizontal axis and extend from 100 s to 200 s, representing the car's constant westward velocity. The two segments should be of equal length since the car travels for 100 seconds in each direction. Signup and view all the answers

A canoeist paddles upstream at a velocity of 2.0 m/s for 4.0 s and then floats downstream at 4.0 m/s for 4.0 s. What is the average velocity of the canoe during the 8.0-s time interval? Choose a coordinate system with the positive direction upstream.

-1.0 m/s Signup and view all the answers

A canoeist paddles upstream at a velocity of 2.0 m/s for 4.0 s and then floats downstream at 4.0 m/s for 4.0 s. What is the average acceleration of the canoe during the 8.0-s time interval?

0.75 m/s^2 downstream Signup and view all the answers

A police officer clocked a driver going 32 km/h over the speed limit just as the driver passed a slower car. When the officer stopped the car, the driver argued that the other driver should get a ticket as well. The driver said that the cars must have been going the same speed because they were observed next to each other. Is the driver correct?

False Signup and view all the answers

If a car accelerates from rest at a constant rate of 5.5 m/s² north, how long will it take for the car to reach a velocity of 28 m/s north?

5.1 s Signup and view all the answers

A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s². How many seconds are required before the car is traveling at a forward velocity of 3.0 m/s? Let the forward direction be positive.

9.0 s Signup and view all the answers

The graph in Figure 13 describes the motion of two bicyclists, Akiko and Brian, who start from rest and travel north, increasing their speed with a constant acceleration. What was the total displacement of each bicyclist during the time shown for each?

Akiko's total displacement is 9.0 m north. Brian's total displacement is 8.0 m north. Signup and view all the answers

Study Notes

Motion Diagrams

Velocity vectors are used to indicate the direction and magnitude of the velocity of an object at an instant in time.
The length of the velocity arrow represents the magnitude of the velocity.
The direction of the velocity arrow represents the direction of motion.

Train's Speed

The train's speed is constant during the time intervals between the times 1 s and 2 s, 3 s and 5 s, and from 6 s to 8 s.

Train's Acceleration

The train's acceleration is positive during the time intervals between the times 0.0 s and 1.0 s, and between the times 5.0 s and 6.0 s.
The train's acceleration is most negative between 2.0 s and 3.0 s because the slope of the graph is the steepest during this interval.

Average Acceleration

The average acceleration of the train during the time interval between 0.0 s to 5.0 s is calculated as follows:
- Average acceleration = change in velocity / time interval
- Average acceleration = (2.5 m/s - 0.0 m/s) / 5.0 s = 0.50 m/s2

Race Car Acceleration

The race car's average acceleration is:
- Average acceleration = (36 m/s - 4.0 m/s) / 4.0 s = 8.0 m/s2
The average acceleration of the car while slowing down is:
- Average acceleration = (15 m/s - 36 m/s) / 3.0 s = -7.0 m/s2

Bus Acceleration

The average acceleration of the bus while braking is:
- Average acceleration = (0.0 m/s - 25 m/s) / 3.0 s = -8.3 m/s2
If the bus took twice as long to stop, the average acceleration would be half as great. This is because acceleration is inversely proportional to the time interval.

Car Acceleration

Choosing uphill as the positive direction, the car's average acceleration can be calculated as follows:
- Average acceleration = (4.5 m/s - (-3.0 m/s)) / 2.5 s = 2.9 m/s2

Jogger Acceleration

Rohith's average acceleration during the 10.0 s interval is:
- Average acceleration = (0.75 m/s - 3.5 m/s) / 10.0 s = -0.28 m/s2

Continental Drift Acceleration

The average acceleration of continental drift over the year is:
- Average acceleration = (0.5 cm/y - 1.0 cm/y) / 1.0 y = - 0.5 cm/y2

Accelerating Objects

Objects can accelerate in three ways:
- by changing their speed,
- by changing their direction,
- or by changing both speed and direction.

Jogger Position-Time Graphs

The position-time graphs of the two joggers will be parallel lines, but the joggers will start at different positions due to their initial difference in position at t = 0.

Jogger Velocity-Time Graphs

The velocity-time graphs of the two joggers will be identical horizontal lines because they are moving at the same constant speed and in the same direction.

Car Velocity-Time Graph

The car's velocity-time graph will be a horizontal line at 25 m/s for the first 100 s.
Next, the graph will drop down to a horizontal line at -25 m/s for the next 100 s.

Canoe Velocity

The average velocity of the canoe during the 8.0 s time interval will be:
- Average velocity = (total displacement) / (time interval)
- Average velocity = (0 m) / (8.0 s) = 0 m/s

Canoe Acceleration

The average acceleration of the canoe during the 8.0 s time interval will be:
- Average acceleration = (change in velocity) / (time interval)
- Average acceleration = (-4.0 m/s - 2.0 m/s) / 8.0 s = - 0.75 m/s2.
- The negative sign indicates that the canoe's velocity is decreasing, which means the canoe is slowing down as it paddles upstream.

Police Officer

The driver is incorrect because the police officer measured the speed of the car using a radar gun. The two cars may have been traveling at the same speed at that instant but had different speeds before.

Car Acceleration - Time to Reach Velocity

The car will take:
- Time = (change in velocity) / (average acceleration)
- Time = (28 m/s - 0 m/s) / (5.5 m/s2) = 5.1 seconds

Car Acceleration - Time to Slow Down

To determine the time it takes for the car to slow down, we can use the following equation:
- Time = (change in velocity) / (average acceleration)
- Time = (3.0 m/s - 22 m/s) / (-2.1 m/s2) = 9.0 seconds

Bicyclist Displacement

Calculate the total displacement of each bicyclist by finding the area under their respective velocity-time graphs.
The area under the graph represents the total distance traveled.
Keep in mind that the displacement and distance traveled can be the same in this case because both cyclists travel in a single direction.

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Description

Test your understanding of accelerated motion concepts including velocity-time graphs, constant speed, and average acceleration. This quiz features various practice problems that require you to analyze different acceleration scenarios, including those of a train and an elevator. Prepare to apply your physics knowledge and enhance your problem-solving skills.