Question

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

• A. Remains same
• B. Becomes one-third of the initial kinetic energy
• C. Becomes nine times the initial kinetic energy
• D. Becomes thrice of the initial kinetic energy

Answer 1

The correct option is C

Becomes nine 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 thrice its initial velocity, then, $v=3u$.
The corresponding change in its kinetic energy is

$K{E}^{\prime }=\frac{1}{2}m{\left(3u\right)}^2=9\times \frac{1}{2}m{u}^2=9KE$

Therefore, the kinetic energy becomes 9 times the initial kinetic energy.