Question

A missile has been fired with an initial velocity $u.$ If the velocity is quadruple, what will be the corresponding change in its kinetic energy?

• A. Becomes thrice of the initial kinetic energy.
• B. Becomes four times of the initial kinetic energy.
• C. Remains constant.
• D. Becomes sixteen times the initial kinetic energy.

Answer 1

The correct option is D Becomes sixteen times the initial kinetic energy.

Kinetic energy of an object, $KE=\frac{1}{2}m{v}^2$, where m is the mass of the object and v is the velocity of the object.

Given: Initial velocity is $u$.
So, initial kinetic energy $KE=\frac{1}{2}m{u}^2$

If the velocity of the object becomes quadruple its initial velocity, then, $v=4u$.
The corresponding change in its kinetic energy is

$K{E}^{\prime }=\frac{1}{2}m{\left(4u\right)}^2=16\times \frac{1}{2}m{u}^2=16KE$

Therefore, the kinetic energy becomes $16$ times the initial kinetic energy.