How to solve this physics problem?

Question

For some odd reason, you decide to throw baseballs at a car of mass M, which is free to move frictionlessly on the ground. You throw the balls at the back of the car at speed u, and at a mass rate of sigma kg/s. If the car starts at rest, find its speed and position as a function of time, assuming that the back window is open, so that the balls collect inside the car.

Answer 1

The problem here is that as the car begins to pick up speed, the transfer of momentum from ball to car goes down, resulting in less force and less acceleration.

A further complication is that the mass M does not remain constant, but increases with each ball added.

Good luck.........

Answer 2

t=0