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Consider three mass m carts equally spaced at rest on a straight
horizontal track. You start pushing an end cart with a force of
magnitude F toward the middle cart and keep doing so. As soon as you
start pushing, the center of mass of the set of three carts starts
experiencing an acceleration of F/(3m) in the direction in which you are
pushing even though the middle cart is experiencing no acceleration
until the one you are pushing is bumping into it.