Question

A car is accelerated on a road and it attains a velocity $3$ times of the initial velocity. In this process the kinetic energy of the car

• A. does not change.
• B. becomes $3$ times that of the initial.
• C. becomes $9$ times that of the initial.
• D. becomes $27$ times that of the initial.

Answer 1

The correct option is C becomes $9$ times that of the initial.

Let the mass of the car be $m$ and its initial speed be $u$ and final speed be $v$.

From the data given in the question, Car is accelerated and final velocity of car is $3$ times its initial velocity.., i.e $v=3u........\left(1\right)$

From the definition of kinetic energy,

Initial kinetic energy of car , $K_i=\frac{1}{2}m{u}^2$

Final kinetic energy of car , $K_f=\frac{1}{2}m{v}^2$

Substituting $\left(1\right)$ in the above equation we get,

$K_f=\frac{1}{2}m\times (3u{)}^2=9\times \left(\frac{1}{2}m{u}^2\right)$

$\Rightarrow K_f=9\times K_i$

Hence, option (c) is the correct answer.

Note: Acceleration $\left(a\right)$ is the rate of change of velocity of an object. $$a=\frac{dv}{dt}$$