With what speed should a stone be thrown along the horizontal surface of the roller so that it, sliding with an acceleration

With what speed should a stone be thrown along the horizontal surface of the roller so that it, sliding with an acceleration of 0.5 m / s2, stops at a distance of 100 m from the initial position?

Given:

L = 100 meters – the distance at which the thrown stone should stop;

a = 0.5 m / s2 – acceleration of the stone.

It is required to determine v0 (meter per second) – at what speed you need to throw a stone

To determine the speed of a stone, you need to use the following formula:

L = v0 * t – a * t ^ 2/2.

Since the stone stops during the movement, we get: t = v0 / a, or:

L = v0 * v0 / a – v0 ^ 2 / (2 * a) = v0 ^ 2 / (2 * a). From here we find that:

v0 = (2 * a * L) ^ 0.5 = (2 * 100 * 0.5) ^ 0.5 = (200 * 0.5) ^ 0.5 = 100 ^ 0.5 = 10 m / s …

Answer: the stone must be thrown at a speed of 10 m / s.