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.