A body with a mass of 100 kg moves in a straight line according to the law S = 5t ^ 2-2.

A body with a mass of 100 kg moves in a straight line according to the law S = 5t ^ 2-2. Find the kinetic energy of the body 2s after the start of the movement.

m = 100 kg.

S (t) = 5 * t ^ 2 – 2.

t = 2 s.

Ek -?

The kinetic energy Ek of a moving body is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of the body, V is the speed of movement.

The dependence of the speed of movement V (t) is the derivative of the dependence of the path covered by the body S (t) “: V (t) = S (t)”.

Find the derivative: V (t) = (5 * t ^ 2 – 2) “= 5 * 2 * t.

Let’s find the speed of the body in t = 2 s from the beginning of the movement: V (2 s) = 5 * 2 * 2 = 20 m / s.

Ek = 0.1 kg * (20 m / s) ^ 2/2 = 20 J.

Answer: the kinetic energy of the body is Ek = 20 J.