# By how much will the kinetic energy of the body increase if its speed is doubled

Kinetic energy of a body depends on its mass and its speed.

KE = (1/2).m.(v^2)

where m = mass of the body

v = speed/velocity of the body

Now, speed is doubled. So, v’ = 2v

Therefore, new kinetic energy will be

KE’ = (1/2).m.(v’^2)

KE’ = (1/2).m.[(2v)^2]

KE’ = (1/2).m.(4v^2)

KE’ = 4 [(1/2).m.(v^2)]

KE’ = 4 KE

Hence, ,kinetic energy will become 4 times the original kinetic energy if the speed is doubled.