Question

A car is accelerated on a levelled road and attains a speed of $5$ times its initial speed. In this process , the kinetic energy of the car:

• A. does not change
• B. becomes $4$ times that of initial kinetic energy
• C. becomes $8$ times that of initial kinetic energy
• D. becomes $25$ times that of initial kinetic energy

Answer 1

The correct option is D becomes $25$ times that of initial kinetic energy

Lets initial velocity of car is $v$, final velocity of this car will be $5v$

$K.E=\frac{1}{2}$ $m{v}^2$

$\therefore K.E\propto v^2$

$K.E_f=K.E_i{\left(\frac{v_f}{v_i}\right)}^2$ where $f$ stand for final and $i$ for initial.

$K.E_f=K.E_i{\left(\frac{5v}{v}\right)}^2=25K.E_i$

So, when the speed increases to 5 times of its initial velocity, the kinetic energy will become 25 times.

The correct answer is d) becomes $25$ times that of initial kinetic energy