By how much will the kinetic energy of a body increase if its speed is doubled?

Expression for the kinetic energy is $K=\frac{1}{2}mv^2$

Here, $K\rightarrow$ kinetic energy of the body

$m\rightarrow$mass of the body

$v\rightarrow$ velocity of the body

On doubling the velocity of the body:

On doubling the velocity, it becomes $2v$

Then kinetic energy of the body $K''=\frac{1}{2}m(2v)^2$

Or $K"=4\times\frac{1}{2}mv^2$

Or $K"=4K$

Thus, on doubling the velocity of the body, its kinetic energy becomes four times.

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Updated on: 10-Oct-2022

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