For 2 s of rectilinear uniformly accelerated motion, the body passed 20 m, and its speed

For 2 s of rectilinear uniformly accelerated motion, the body passed 20 m, and its speed increased 3 times. Determine the acceleration of the body.

Given:

t = 2 seconds – time interval;

S = 20 meters – the distance traveled by the body during the time interval t;

v = 3 * v0 – during the time t the body’s speed increased 3 times.

It is required to determine a (meter per second squared) – the acceleration of the body.

Equally accelerated motion is determined by the following formula:

S = v0 * t + a * t ^ 2/2 (1).

From the acceleration formula we find that:

a = (v – v0) / t = (3 * v0 – v0) / t = 2 * v0 / t, hence:

v0 = a * t / 2.

Substituting the value of the initial speed into the formula (1), we get:

S = a * t ^ 2/2 + a * t ^ 2/2 = 2 * a * t2 / 2 = a * t ^ 2, hence:

a = S / t ^ 2 = 20/22 = 20/4 = 5 m / s2.

Answer: the body moves with an acceleration equal to 5 m / s2.