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# The kinetic energy of an object of mass, m moving with a velocity of 5 m s^-1 is 25 J. What will be its kinetic energy when its velocity is doubled?

The kinetic energy of an object of mass, $m$ moving with a velocity of $5 \; m\; s ^{-1}$  is $25\; J$. What will be its kinetic energy when its velocity is doubled?

What will be its kinetic energy when its velocity is increased three times?

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Using the formula for the kinetic energy we have :

$K.E\ =\ \frac{1}{2}mv^2$

or                                                           $25\ =\ \frac{1}{2}m\times 5^2$

or                                                             $m\ =\ 2\ Kg$

(i) Kinetic energy when velocity is doubled :

$K.E\ =\ \frac{1}{2}mv^2$

$=\ \frac{1}{2}\times2 \times 10^2$

$=\ 100\ J$

(ii) Kinetic energy when velocity is tripled :

$K.E\ =\ \frac{1}{2}mv^2$

$=\ \frac{1}{2}\times 2\times 15^2$

or                                                                 $=\ 225\ J$

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