The kinetic energy of an object of mass m,

Question.
The kinetic energy of an object of mass m, moving with a velocity of $5 \mathrm{~ms}^{-1}$ is $25 \mathrm{~J}$. What will be its kinetic energy when its velocity is doubled ? What will be its kinetic energy when its velocity is increased three times?

Solution:

Given, velocity of object, $\mathrm{v}=5 \mathrm{~ms}^{-1}$;

kinetic energy of an object, $\mathrm{E}_{\mathrm{K}}=25 \mathrm{~J}$

$E_{K}=\frac{1}{2} m v^{2} \quad$ or $\quad 25=\frac{1}{2} \times m \times(5)^{2}$

or $\mathrm{m}=\frac{50}{25}=2 \mathrm{~kg}$

When the velocity doubles,

$E_{K}=\frac{1}{2} m v^{2}=\frac{1}{2} \times 2 \times(10)^{2}=100 J$

When the velocity triples,

$E_{K}=\frac{1}{2} m v^{2}=\frac{1}{2} \times 2 \times(15)^{2}=225 \mathbf{J}$

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