21. If an object’s speed is doubled, how does its Kinetic Energy change?

Hello!

For an object with a mass `m` and a speed `V` its kinetic energy is defined as

`E_k=m V^2/2.`

So if a speed is doubled, `V_1=2V,` and a mass remains unchanged, then

`(E_k)_1=m (V_1)^2/2 = m (2V)^2/2=4*(m V^2/2)=4E_k.`

Thus the kinetic energy will be quadrupled (4 times greater than the original).