The body moves uniformly at a speed of 8 m / s for 10 s, after which it receives an acceleration of 2 m / s.

The body moves uniformly at a speed of 8 m / s for 10 s, after which it receives an acceleration of 2 m / s. What speed will the body have in 15 s from the beginning of the movement? What path will it take during the entire movement?

Given:

v = 8 meters per second – initial speed of the body;

t1 = 10 seconds – the time during which the body moved uniformly;

a = 2 m / s2 – body acceleration;

t2 = 15 seconds – time span.

It is required to determine v (m / s) – the speed of the body after a time interval t2 from the beginning of movement, and S (meter) – the path traversed by the body.

Let us find the time interval during which the body was moving uniformly accelerated:

t3 = t2 – t1 = 15 – 10 = 5 seconds.

Then the speed of the body will be equal to:

v = v0 + a * t3 = 8 + 2 * 5 = 8 + 10 = 18 m / s.

Since the movement of the body consisted of two components: uniform and uniformly accelerated, the total distance traveled will be equal to:

S = S1 + S2;

S = v0 * t1 + v0 * t3 + a * t3 ^ 2/2 = 8 * 10 + 8 * 5 + 2 * 5 ^ 2/2 =

= 80 + 40 + 25 = 120 + 25 = 145 meters.

Answer: the speed of the body will be 18 m / s, the total distance traveled is 145 meters.