Question

What will happen to the kinetic energy of a body if its velocity is doubled?

Answer 1

$kinetic \: energy = \frac{1}{2} m {v}^{2}$
so kinetic energy is directly proportional to v^2
coz mass is constant
so new kinetic energy changes as (2v)^2 =4v^2
so kinetic energy increases 4 times

Answer 2

Kinetic Energy becomes four times the initial value.

Let's see a detailed explanation:

The general expression of Kinetic Energy is:

$\boxed{KE = \dfrac{1}{2} m {v}^{2} }$

• 'm' is mass and 'v' is velocity.

Now, as per the question, the new velocity is doubled (i.e 2v)

So, new kinetic energy is :

$KE_{2} = \dfrac{1}{2} \times m\times {(2v)}^{2}$

$\implies KE_{2} = \dfrac{1}{2} \times m\times 4 {v}^{2}$

$\implies KE_{2} = 4 \times \dfrac{1}{2} \times m\times {v}^{2}$

$\implies KE_{2} = 4 \times (\dfrac{1}{2} m {v}^{2} )$

$\implies KE_{2} = 4 \times KE$

So, new kinetic energy is 4 times the initial value.