Question

What happens to the kinetic energy when velocity of body is doubled at constant mass?

Answer 1

The kinetic energy increases by four times (becomes 4 times).

Mathematical Derivation:

Original Kinetic Energy:

\[ K = \frac{1}{2}mv^{2} \]

Substituting new velocity \(v' = 2v\) and keeping mass \(m' = m\):

\[ K' = \frac{1}{2}m(2v)^{2} \]

\[ = \frac{1}{2}m(4v^{2}) \]

\[ = 4 \times \left(\frac{1}{2}mv^{2}\right) \]

= 4 K