Finding the ratio of masses in constant acceleration motion

[Victorzaroni]

Homework Statement

An engine provides a constant force F to a car of mass M that carries a box of mass m on the top of it. After traveling from rest with constant acceleration a₁ for 20 seconds, the speed of the car becomes 40m/s and at that instant the box falls off the car. In the next 20 seconds, with force F remaining constant, the car travels with constant acceleration, a₂, 1280 meters from the point the box fell.

The ratio of the accelerations a₂/a₁ would be:

I got 1.2, which is correct.


The ratio m/M would be:

The answer is (a₂-a₁)/a₁, I just don't know how to get there.

Homework Equations

F=MA

The Attempt at a Solution

I have a feeling this is simple, but I can't seem to work it out.

 

[Alucinor]

Well, you know that the force is constant the whole time. So the force when the box is on the car is the same as when the box is off the car.

Think of the first situation as the box + car situation. Then the second situation is only the car.

Remember that $$F_{engine}$$ is constant.

Try working from there