Question 3
The kinetic energy of an object of mass, m moving with a velocity of $5m{s}^{-1}$ is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

K.E. of the object = 25 J
Velocity of the object, $v=5m{s}^{-1}$
$\because K.E.=\frac{1}{2}m{v}^2$
$\Rightarrow m=\frac{2K.E.}{v^2}$
$\Rightarrow m=2\times \frac{25}{25}=2kg$

If the velocity is doubled,$v=2\times 5=10m{s}^{-1}$
$\therefore K.E.(forv=10m{s}^{-1})=\frac{1}{2}\times 2\times 100=100J$

If the velocity is tripled, $v=3\times 5=15m{s}^{-1}$
$\therefore K.E.(forv=15m{s}^{-1})=\frac{1}{2}\times 2\times 225=225J$