Figure 2.3: The net displacement is still –5 m, even though the path taken from to is different from the direct path taken in Figure 2.2.
EXAMPLE 2.1 – Interpreting graphs
Another way to represent positions and displacements is to graph the position as a function of time, as in Figure 2.4. This graph could represent your motion along a sidewalk.
(a) What happens at a time of t = 40 s?
(b) Draw a diagram similar to that in Figure 2.3, to show your motion along the sidewalk. Add circles to your diagram to show your location at 10-second intervals, starting at t = 0.
Using the graph in Figure 2.4, find (c) your net displacement and (d) the total distance you covered during the 50- second period.
SOLUTION
(a) At a time of t = 40 s, the graph shows that your motion changes from travel in the positive x-direction to travel in the negative x-direction. In other words, at t = 40 s you reverse direction.
Figure 2.4: A graph of the position of an object versus time over a 50-second period. The graph represents your motion in a straight line as you travel along a sidewalk.
(b) Figure 2.5 shows one way to turn the graph in Figure 2.4 into
a vector diagram to show how a series of individual displacements adds together to a net displacement. Figure 2.5 shows five separate displacements, which break your motion down into 10-second intervals.
(c) The displacement can be found by subtracting the initial position, +20 m, from the final position, +60 m. This gives a net displacement of
.
A second way to find the net displacement is to recognize that the motion consists of two displacements, one of +80 m (from +20 m to +100 m) and one of –40 m (from +100 m to +60 m). Adding these individual displacements gives .
(d) The total distance covered is the sum of the magnitudes of the individual displacements. Total distance = 80 m + 40 m = 120 m.
Related End-of-Chapter Exercises: 7 and 9
Essential Question 2.1: In the previous example, the magnitude of the displacement is less than the total distance covered. Could the magnitude of the displacement ever be larger than the total distance covered? Could they be equal? Explain. (The answer is at the top of the next page.)
Figure 2.5: A vector diagram to show your displacement, as a sequence of five 10-second displacements over a 50-second period. The circles show your position at 10-second intervals.
Chapter 2 – Motion in One Dimension
Page 2 - 3