The body, moving uniformly accelerated from the state of rest, passed the path S1 = 10m in time t = 2s.

The body, moving uniformly accelerated from the state of rest, passed the path S1 = 10m in time t = 2s. What speed V will this body have when the path traversed since the start of movement is S2 = 40m?

Given:

S1 = 10 meters – let, which the body has passed during the time interval t;

t = 2 seconds – time interval;

S2 = 40 meters.

It is required to determine v (m / s) – the speed that the body will have when the distance traveled is equal to S2.

According to the condition of the problem, the movement of the body was uniformly accelerated. Also, the body moved from a state of rest, that is, without an initial speed. Then, we find the acceleration of the body:

a = 2 * S1 / t ^ 2 = 2 * 10/2 ^ 2 = 20/4 = 5 m / s2.

The time it takes for the body to cover the path S2 will be equal to:

t2 = (2 * S2 / a) ^ 0.5 = (2 * 40/5) ^ 0.5 = (80/5) ^ 0.5 = 160.6 = 4 seconds.

Then the speed of the body will be equal to:

v = a * t ^ 2 = 5 * 4 = 20 m / s.

Answer: the speed of the body will be equal to 20 m / s.