Finding the Speed of a head hit by a soccer ball

[HappyFlower]

Homework Statement

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 2-38 gives the measured acceleration a(t) of a soccer player's head for a bare head and a helmeted head, starting from rest. At time t = 7 .0 ms, what is the difference in the speed acquired by the bare head and the speed acquired by the helmetedhead?

Homework Equations

The Attempt at a Solution

I uploaded the picture of the graph and question also I was able to get an answer. I found the peak of the helmet graph to be 80 m/s^2 and .006s. I found the other peak from the bare graph to be 200 m/s^2 and .006s.
I multiplied 80 m/s^2 * .006s=.48 m/s and 200 m/s^2 *.006s =1.2 m/s
1.2 m/s- .48 m/s =.57 m/s
the answer of the problem is .56 m/s, I was wondering if I did the problem the right way?

 

[kuruman]

The final velocity is the area under each curve v = ∫a dt. You have a whole bunch of triangle and rectangle areas to calculate. Go for it.

 

[haruspex]

As an aside, the graph completely misrepresents reality. The player intends to impart a specific impulse to the ball. If that is being achieved in both graphs then the helmet must be heavier than the head!
The real benefit of the helmet is the extent to which it spreads the impulse over a longer duration.