What happens to kinetic energy when mass and velocity is halved?

Text Solution

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Solution : Suppose Initial mass `(m _(1)) = m kg` <br> Initial velocity `(v _(1)) = v m//s` <br> Given `m _(2) = 2m kg ` <br> `v _(2) = 2v m//s` <br> Initial kinetic energy, `K _(1) = (1)/(2) mv ^(2) ...(1)` <br> Final kinetic energy, `K _(2) = (1)/(2) xx 2m xx 4v ^(2)` <br> `(K _(1))/( K _(2)) = (1 xx mv ^(2)) /( 2 xx 4 mv ^(2)) ....(2)` <br> `= 1/8` <br> `K _(2) = 8 K _(1)`

Solutions:

If the speed is halved while the mass remains the same, the kinetic energy drops. Because kinetic energy is related to velocity squared, it is one-fourth.

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