Question: A ball bearing rests on a ramp fixed to the top of a car which is
accelerating horizontally. The position of the ball bearing relative to the
ramp is used as a measure of the acceleration of the car. Show that if
the acceleration is to be proportional to the horizontal distance moved by
the ball (measured relative to the ramp), then the ramp must be curved
upwards in the shape of a parabola. ++
I've done it using a potential energy argument but I'm not quite sure if it's correct. Any ideas?