A bat hits a ball; which has the greater acceleration, the bat or the ball? The bat because it has a larger mass than the ball. The ball because it has a smaller mass than the bat. Although the ball has a smaller mass than the bat, they both have the same magnitude of acceleration.

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AL2006

A bat hits a ball.  

We know from Newton #3 that the same size force acts on both objects.

The ball has the greater acceleration, because the ball has less mass than the bat has, and the same force acting on a smaller mass produces a greater acceleration.