How does the body move if its velocity is given by the equation v = 10t? determine the movement of the body in 4 s.

Given:

v (t) = 10 * t – dependence of speed on time;

t = 4 seconds.

It is required to determine the nature of the movement of the body, as well as the movement of the body S (meters) during time t.

Let’s find the acceleration of the body:

a (t) = v (t) ‘= (10 * t)’ = 10 m / s ^ 2.

Let’s find the speed of the body at the initial moment of time t = 0:

v (0) = 10 * 0 = 0

It can be seen that the acceleration of the body is constant and equal to 10 m / s ^ 2. This means that the body is moving uniformly accelerated without initial velocity.

The movement of the body will be equal to:

S = a * t ^ 2/2 = 10 * 4 ^ 2/2 = 5 * 4 ^ 2 = 5 * 16 = 80 meters.

Answer: the body moves uniformly accelerated without initial speed, in 4 seconds the body will cover a path equal to 80 meters.