The body moves rectilinearly from a state of rest with constant acceleration. Having passed the distance S = 10 m

The body moves rectilinearly from a state of rest with constant acceleration. Having passed the distance S = 10 m, it acquires a speed of v = 15 m / s. Determine the time of movement and acceleration of the body.

Given:
S = 10 meters – the path covered by the body;
v = 15 meters per second – the speed of the body, which it acquired, having passed the distance S.
It is required to determine t (seconds) – time of body movement, and a (m / s2) – body acceleration.
According to the condition of the problem, the body moves in a straight line from a state of rest, that is, without an initial velocity. Then:
S = a * t ^ 2 / 2.Considering that in this case a = v / t, we get:
S = a * t ^ 2/2 = v * t ^ 2 / (2 * t) = v * t / 2, from here we find that:
t = 2 * S / v = 2 * 10/15 = 20/15 = 1.3 seconds (the result has been rounded to one decimal place).
Then the acceleration of the body will be equal to:
a = v / t = 15 / 1.3 = 11.5 m / s2.
Answer: the time of body movement is 1.3 seconds, the acceleration of the body is 11.5 m / s2.