can a light object that was hit with a small force accelerate as rapidly as a heavier object hit with a big force? why or why not?

The acceleration is defined by force divided by the mass of the object. So, When the smaller object is hit by a small force, it can produce equal acceleration which is same as that of the bigger body hit with large force.

Explanation:

Force is defined as the product of the mass of the body its applied to and the acceleration of the body in the direction of the force. So acceleration is force divided by the mass of the body.

Let the mass of the smaller body be m and that of the larger body be M.

The smaller force applied on the smaller body be f and the larger force applied on the larger body be F.

So acceleration of the larger body = F/M.

Acceleration of the smaller body = f/m.

For the accelerations to be same,

F/M = f/m.

Or F/f = M/m.

So when the ratio of the force applied on two bodies is in ratio of their masses, the acceleration becomes equal.