Momentum and Acceleration

My question is: "How fast does he accelerate?"
I know he doesn't magically go from 0 m/s to 8. Teacher told me you'd need to know more information.

So 1) what else, if anything, do you need to know and 2) how would you work the acceleration out if you had all the required variables?

1) You don't need more information.
2) IF it's completely frictionless, think of Newton's cradle (except that the balls aren't going to slow to a stop). In your example, the ball will just stop moving and the guy will move in the place of the ball. He goes from 0m/s to 8m/s instantaneously. Now, if there were frictional force, using the normal force, you can calculate for the guy's deceleration.

So, you'd need to know the time.

Why do you need to know the time? He's in a frictionless environment. It doesn't matter if it takes 20 seconds for the ball or 30 seconds for the ball to hit the guy, it's still going to hit the guy with 400N.