A body with an initial speed of 2 m / s to a complete stop travels a path of 5 m.

A body with an initial speed of 2 m / s to a complete stop travels a path of 5 m. Is this a body with an initial speed of 4 m / s, will it pass the way to a complete stop?

Given:

v1 = 2 m / s – initial velocity of the body;

S1 = 5 meters – the path that the body takes to a complete stop;

v2 = 4 m / s.

It is required to determine S2 (meters) – the path that the body will travel to a complete stop at an initial speed equal to v2.

Since it is not specified in the problem statement, we assume that the acceleration of the body in both cases will be the same. Then:

S1 = v1 * t – a * t ^ 2/2 = v1 * v1 / a – a * (v1 / a) ^ 2/2 = v1 ^ 2 / a – v1 ^ 2 / (2 * a) = v1 ^ 2 / (2 * a), hence:

a = v1 ^ 2 / (2 * S) = 2 ^ 2 / (2 * 5) = 4/10 = 0.4 m / s2.

Then:

S2 = v2 ^ 2 / (2 * a) = 4 ^ 2 / (2 * 0.4) = 16 / 0.8 = 20 meters.

Answer: the body will travel a distance of 20 meters.