How will the kinetic energy of a body weighing 2 kg change with an increase in speed by 4 times?

Given:

m = 2 kilograms – body weight;

v2 = 4 * v1 – the speed of the body was increased by 4 times.

It is required to determine E2 / E1, how the kinetic energy of the body will change if the speed is increased by 4 times.

In the first case (normal speed), the kinetic energy will be equal to:

E1 = m * v1 ^ 2/2 = 2 * v1 ^ 2/2 = v1 ^ 2.

In the second case (increased speed), the kinetic energy of the body will be equal to:

E2 = m * v2 ^ 2/2 = 2 * v2 ^ 2/2 = v2 ^ 2 = (4 * v1) ^ 2 = 16 * v1 ^ 2.

Then:

E2 / E1 = 16 * v1 ^ 2 / v1 ^ 2 = 16 times.

Answer: the kinetic energy of the body will increase 16 times.