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