Question

A person is pushing on a refrigerator that sits on a level floor. Use Newton's third law along with his second law to find the magnitude of the acceleration of a man as he pushes the refrigerator. Assume the man has a mass of 62 kg, he exerts a force of 128 N, the refrigerator has a mass of 187 kg, and the floor is very slippery so that there is no frictional force between the floor and the man.

Answer 1

F = m a is the equation you use
It's called Newton's second law.

The equation applies bioth to to the man and the refrigerator, but the accelertions of the two are different, since the masses ara different

You want to know the acceleration of the man, a.
So m must be the man's mass, 62 kg
F is the force exerted by the refrigerator on the man, which is -128 N

The minus sign is there if the positive direction is that of the man's force on the refrigerator. The force on the man is equal and opposite. The man accelerates backwards. That is where Newton's Third law is used.

a = -128 N/62 kg = -2.06 m/s^2