A missile is fired with an initial velocity $u .$ If the velocity is tripled, what will be the corresponding change in its kinetic energy? $[1 mark]$

A. It remains the same.
B. It becomes one-third of the initial value.
C. It becomes nine times the initial value.
D. It becomes thrice the initial value.

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Solution

Correct answer $:$ option C $-$ It becomes nine times the initial value.

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

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

If the velocity of the object becomes thrice its initial velocity, then, $v = 3 u$ .
The new kinetic energy is:

$K_{f} = \frac{1}{2} m {(3 u)}^{2} = 9 \times \frac{1}{2} m u^{2} = 9 K_{i}$

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

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A missile is fired with an initial velocity u. If the velocity is tripled, what will be the corresponding change in its kinetic energy? [1 mark] A. It remains the same. B. It becomes one-third of the initial value. C. It becomes nine times the initial value. D. It becomes thrice the initial value.