A mass m is moving with a velocity v and its kinetic energy is K. What will be the new kinetic energy if the velocity is doubled?
4 K
The kinetic energy (K) of an object is given by the formula:
\(K = \frac{1}{2}mv^2\)
where:
- \(m\) is the mass of the object
- \(v\) is the velocity of the object
Initially, the kinetic energy is \(K = \frac{1}{2}mv^2\).
If the velocity is doubled, the new velocity is \(v' = 2v\). The new kinetic energy \(K'\) will be:
\(K' = \frac{1}{2}m(v')^2 = \frac{1}{2}m(2v)^2 = \frac{1}{2}m(4v^2) = 4(\frac{1}{2}mv^2)\)
Since \(K = \frac{1}{2}mv^2\), we can substitute this into the equation for \(K'\):
\(K' = 4K\)
Therefore, if the velocity is doubled, the new kinetic energy will be 4 times the original kinetic energy.
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