Question

Calculate the change in the kinetic energy of a moving body if its velocity is reduced to $1/3rd$ of the initial velocity.

Answer 1

Given: Initial velocity $=v$; Final velocity $=\frac{v}{3}$
Initial kinetic energy $k_1=\frac{1}{2}\times m\times v^2$
Final kinetic energy $k_2=\frac{1}{2}\times m\times {\left(\frac{v}{3}\right)}^2=\frac{1}{9}\times \frac{1}{2}m{v}^2$
Change in kinetic energy $=\frac{1}{2}m{v}^2-\frac{1}{9}\times \frac{1}{2}m{v}^2$
$=\frac{1}{2}m{v}^2(1-\frac{1}{9})$
$=\frac{8}{9}\times \frac{1}{2}\times m{v}^2$
$=\frac{8}{9}\times$ Initial kinetic energy.