By how much will the kinetic energy of a body increase if its speed is doubled?
As
The energy possessed by a body when it is in the state of motion is its kinetic energy.
kinetic energy of a body depends on its mass and its speed.
KE = 
where m = mass of the body
v = speed/velocity of the body
If the velocity has become twice of the previous value and since we can't change the mass of a body its an inherited property of a body. Therefore
Since Kinetic energy = (1/2)mv2 so incase we see the result in respect of the Kinetic energy of the body which, for twice velocity we can easily conclude its KE must have increased by 300% and becomes four times the previous value