PYQ NEET- Work Energy And Power L-3

Question:#

A car accelerates from rest to $\mathrm{u} \mathrm{m} / \mathrm{s}$. The energy spent in this process is $\mathrm{EJ}$. The energy required to accelerate the car from $u \mathrm{~m} / \mathrm{s}$ to $2 u m / \mathrm{s}$ is $n E J$. The value of $n$ is

Answer:#

The kinetic energy of a moving object of mass $m$ and velocity $v$ is given by the formula: $$ K=\frac{1}{2} m v^2 $$

The work done in accelerating an object from rest to velocity $v$ is equal to its change in kinetic energy. Therefore, the energy spent in accelerating the car from rest to $u \mathrm{~m} / \mathrm{s}$ is: $$ E=\frac{1}{2} m u^2 $$

The energy required to accelerate the car from $u \mathrm{~m} / \mathrm{s}$ to $2 u \mathrm{~m} / \mathrm{s}$ is: $$ \begin{aligned} n E & =\frac{1}{2} m(2 u)^2-\frac{1}{2} m u^2 \ & =2 m u^2-\frac{1}{2} m u^2 \ & =\frac{3}{2} m u^2 \ & =3 E \ \therefore \mathrm{n} & =3 \end{aligned} $$