Apply why does a box on the seat of a car slide around on the seat when the car speeds up slows down or turns a corner?

This is because of the first Newton's law:

If an object is at rest or at moving with constant velocity, it will remain doing that untill a force is applied on the object.

Now, if the car is still, and then it speeds, the box will want to keep the movement that it was doing before, so it will slide in the seat until the box gets the same speed as the car (this can happen when the box hits the back of the seat, and the back of the seat "pushes" the box)

Now, the same happens when the car stops, now the box has a velocity and when the car stops the box will keep moving forward, because there is no force that stops the box.