The kinetic energy of a body is proportional to the square of its speed. Determine by what percentage

The kinetic energy of a body is proportional to the square of its speed. Determine by what percentage the kinetic energy of the body will increase if its speed increases by 40%.

We can find the kinetic energy of the body by the formula:

Ek = mV ^ 2/2, where Ek – kinetic energy, m – body mass, V – body speed.

Let’s increase the body speed by 40%, or multiply by 0.4:

Ek40 = m (0.4V) ^ 2/2 = m (0.4V) ^ 2/2 = 0.16mV ^ 2/2

If we divide the kinetic energy before and after the increase in speed, then we get the following expression:

0.16mV ^ 2/2: 6mV ^ 2/2 = 0.16Ek / Ek = 0.16 increase in kinetic energy.

To express this value as a percentage, it must be multiplied by 100:

0.16 * 100 = 16%

Answer: kinetic energy will increase by 16%.