A car accelerates from rest of um s ^ - 1 . The energy spent in...

The kinetic energy of a moving particle is given by

$E = \dfrac{1}{2}m{u}^{2} . . . ( 1 )$

When the final velocity of the particle becomes twice the initial velocity, the kinetic energy of the particle can be written as

$\begin{cases}nE & = & \dfrac{1}{2}m\left\{( 2u{)}^{2} - {u}^{2}\right\} \\ & = & \dfrac{1}{2}m\left(3{u}^{2}\right) . . . \left(2\right)\end{cases}$

Divide equation (2) by equation (1) and solve to calculate the value of $n$.

$\begin{cases}\dfrac{nE}{E} & = & \dfrac{\dfrac{1}{2}m\left(3{u}^{2}\right)}{\dfrac{1}{2}m{u}^{2}} \\ & ⇒ & n = 3\end{cases}$