Question

When the velocity of a body is " trippled" ( from v to 3v ) , then its kinetic energy becomes " nine times" .Why?

Answer 1

Kinetic Energy =
$\frac{1}{2} m {v}^{2}$
When velocity is tripled say v becomes 3v,

Then the kinetic energy will be 1/2*m*(3v)²

= 1/2*m*9v,

So by this we can understand that if velocity becomes tripled the kinetic energy becomes 9 times !

Answer 2

ke=1/2 mv^2
ke directly proposal to v^2