2.1.2 Displacement and Average Velocity

Question 1

Displacement and Average Velocity

Answer 1

• Displacement is a change in position, Df = xf - xi, and it includes both a magnitude and a direction.
• The average velocity is the ratio of the displacement of an object to the time interval required for the displacement: delta = Dx/Dt

Question 2

note

Answer 2

• Displacement is change in position: . (Note: The symbol D means “change in.”) The displacement of the iguanodon as he moves from 4 to 1 is 1 – 4 = –3. The iguanodon’s displacement is in the negative direction and he moves 3 units.
• Distance is the length of the entire path traveled. The iguanodon moves from –1 to 1. He turns around and moves back to 0. He turns again and moves to 2. The distance traveled by the iguanodon is 5. The iguanodon’s displacement is determined by simply subtracting his initial position from his final position: 2 – (–1) = 3. In general, displacement is a more useful quantity than distance in physics problems.
• The average velocity is the ratio of displacement to the amount of time required for the displacement: .Suppose that the iguanodon runs at a constant rate as shown in the graph on the left. He completes a 25 mile race in 0.5hour, so his average velocity for the race is 50 mph. Notice that for uniform motion, average velocity is the slope of the position function and can be measured anywhere along the path.
• A ball falls to the ground with nonuniform velocity as shown by the parabolic function in the graphs. The average velocity of the ball changes depending on the interval over which it is measured. In the graph on the right, the slope of the lower secant represents the average velocity during the first half of the ball’s fall, and the slope of the upper secant represents the average velocity of the ball during the second half of the fall. Notice that the slope of the lower secant is shallower than the slope of the upper secant. Likewise the average velocity of the ball is less for the first half of the fall than for the second half of the fall

Question 3

Suppose that Jamie drives from town to town for his job. Over the course of a day, Jamie visits each of the four towns indicated. His itinerary is shown. Jamie begins his day in Orston and finishes his work travel in Port Mills. Which of the following statements about his work day is not correct?

Answer 3

Jamie’s total distance traveled is 25 km.

Question 4

Suppose a train travels in a straight line between two towns. During the course of the trip, the train stops, backs up a short distance, and eventually resumes moving forward toward the other town. Which of the following statements related to the displacement of the train is not correct?

Answer 4

The total distance traveled is equal to the distance between the two towns.

Question 5

In Event 1, an object has uniform motion in one direction. In Event 2, the same object has the same uniform motion in the opposite direction. Which of the following statements correctly describes the two events?

Answer 5

The average velocity is negative for Event 2 and positive for Event 1.

Question 6

Which of the following statements is not correct?

Answer 6

Displacement is the same as the total distance travelled.

Question 7

Suppose a train starts at point −3. It moves to point +5, rests, and then proceeds to point +8. Later it moves backwards to point −1, then finally stops at point +1. Which of the following is the displacement for the train and the distance traveled by the train?

Answer 7

None of the above

Question 8

Which of the following best defines the displacement of an object?

Answer 8

The net change in position

Question 9

The Kleber family took a car trip one day that lasted 6 hours as shown on the graph. Which of the following statements about the Kleber’s trip is correct?

Answer 9

During the first part of their trip, the average velocity was 50 km / h. Their average velocity between 4 and 6 hours was 75 km / h.

Question 10

The graph shows the motion of a falling ball during the interval from t0 to t5. During which interval is the average speed the greatest? During which interval is the average speed the least? Why is the plot a curve instead of a straight line?

Answer 10

The average speed is greatest between t4 and t5. The average speed is least between t0 and t1. The plot is a curve because the ball does not fall with uniform motion.

Question 11

In which of the following is the magnitude of the displacement different from the distance?

Answer 11

Driving in a car as you run errands over the course of 3 hours and then returning to where you started.