The distance between a toy car’s axes is L, the center of mass is equally distanced from the axes and it is at a height h from the horizontal plane. The front wheels of the car can freely turn and their masses are insignificant. The rear wheels, however, do not turn at all. The car is lying on a horizontal plane, the coefficient of friction between the wheel and the horizontal plane is μ and the gravitational acceleration is g.
The horizontal plane starts to move back and forth with a high frequency. At the first half-period the surface’s velocity vector is directed from the car’s rear wheel towards the front wheel and at the second half-period the direction is the opposite; during both of the half-periods the speed stays constant; during the oscillation the surface is moved so fast that the car always slides either one way or another with respect to the surface. With what average acceleration does the car start to move?