A ball moves in a straight line (the x-axis). The graph in ?Fig. E2.9 shows this ball’s velocity as a function of time. (a) What are the ball’s average speed and average velocity during the first 3.0 s? (b) Suppose that the ball moved in such a way that the graph segment after 2.0 s was - 3.0 m/s instead of + 3.0 m/s. Find the ball’s average speed and average velocity in this case.

Solution 9E Step 1: a) Average speed, s = Total distance travelled by the object/Total time In this problem, the velocity of the ball in first two seconds is, v = 2 m/s 1 Therefore, the total distance travelled by the object at first two seconds, d = v t 1 1 1 d = 2 m/s × 2 s = 4 m 1 The total distance travelled by the object in between 2nd and 3rd second is, d = v t 2 2 2 d = 3 m/s × 1 s = 3 m 2 Therefore, the total distance travelled by the object, d = d + d = 4 m + 3 m = 7 1 2 Total time taken, t = t + t =1 s +2 s = 3 s Average speed of the ball, s = 7 m / 3 s = 2.33 m/s