# By how many times will the kinetic energy of a body increase if it's speed is tripled? Show by calculation.

Velocity,v = v

K.E[1] = 1/2 x m x [v]^2

K.E.[1] = 1/2 m v^2

When velocity,v is tripled then,

Mass,m = m

Velocity,v = 3v

K.E [2].= 1/2 x m x [v]^2

K.E.[2] = 1/2 x m x [3v]^2

K.E.[2] = 1/2 x m x 9v^2

K.E.[2] = 1/2 m 9v^2

Ratio of K.E. [1] and [2],

1/2 x m x v^2 / 1/2 x m x 9v^2

v^2 / 9v^2

1 /9 or 1 : 9

Hence, K.E. will increase by 9 times if it's speed is tripled.