Walker, Halliday & Resnick — Motion Along a Straight Line: Problem 67

67 When a soccer ball is kicked toward a player and the player deflects the ball by “heading” it, the acceleration of the head during the collision can be significant. Figure 2-23 gives the measured acceleration \( a(t) \) of a soccer player’s head for a bare head and a helmeted head, starting from rest. The scaling on the vertical axis is set by \( a_s = 200 \text{ m/s}^2 \). At time \( t = 7.0 \text{ ms} \), what is the difference in the speed acquired by the bare head and the speed acquired by the helmeted head?