The body, moving evenly, travels 35 cm in 7 seconds, after which it begins to move evenly-accelerated

The body, moving evenly, travels 35 cm in 7 seconds, after which it begins to move evenly-accelerated and in 5 seconds it passes 1.5 m. Determine the speed at the end of the path and acceleration?

Given:

S = 35 centimeters = 0.35 meters – movement of the body with uniform movement;

t = 7 seconds – time of uniform movement;

S1 = 1.5 meters – movement with uniformly accelerated movement;

t1 = 5 seconds – time of uniformly accelerated movement.

It is necessary to find the speed at the end of the path V (m / s) and the body’s acceleration a (m / s ^ 2).

The body speed with uniform movement will be:

V0 = S / t = 0.35 / 7 = 0.05 m / s.

Find the acceleration:

S1 = V0 * t1 + a * t1 ^ 2/2

1.5 = 0.05 * 5 + a * 5 * 5/2

1.5 = 0.25 + 12.5 * a

12.5 * a = 1.25

a = 1.25 / 12.5 = 0.1 m / s ^ 2.

Find the speed at the end of the path:

V1 = V0 + a * t1 = 0.05 + 0.1 * 5 = 0.05 + 0.5 = 0.55 m / s.

Answer: the acceleration of the body is 0.1 m / s ^ 2, the speed of the body at the end of the path is 0.55 m / s.