Even without the equations, it is not difficult to describe how such a motion is possible.

For one, the assertion relates to the curve with a vertical cusp: y3 = x2. Also, the initial speed as assumed non-zero.

Now, say, if the particle moves rightwards, the gravitational force acts to slow it down but the farther it moves from the origin, the less the effect of the gravitational force becomes. For this particular curve it is claimed that in the same amount of time, although the horizontal distance covered will grow with the distance from the origin, the vertical distance will remain the same.