91Ó°ÊÓ

The energy possessed by an object by virtue of its motion is called kinetic energy.For example, the motion of a yo-yo, stretching a rubber band, moving the muscles, a moving car, etc.

The kinetic energy is proportional to the mass and square of the velocity of the object. Its formula is given by:

\(KE = \frac{1}{2}m{v^2}\)

Here, m is the mass of the object, and vis the velocity.

The change in the kinetic energy is given by:

\(KE = \frac{1}{2}m\left( {v_2^2 - v_1^2} \right)\)

Here,\({v_1} = 0\)and\({v_2} = 30\;{\rm{km/h}}\).

Therefore, the change in energy will be:

\(\begin{aligned}KE &= \frac{1}{2}m\left( {{{\left( {30\;{\rm{km/h}}} \right)}^2} - {{\left( 0 \right)}^2}} \right)\\ &= \frac{1}{2}m\left( {900} \right)\\ &= 450m\end{aligned}\)

The change in the kinetic energy is given by:

\(KE = \frac{1}{2}m\left( {v_2^2 - v_1^2} \right)\)

Here,\({v_1} = 30\;{\rm{km/h}}\)and\({v_2} = 60\;{\rm{km/h}}\).

Therefore, the change in energy will be:

\(\begin{aligned}KE &= \frac{1}{2}m\left( {{{\left( {60\;{\rm{km/h}}} \right)}^2} - {{\left( {30\;{\rm{km/h}}} \right)}^2}} \right)\\ &= \frac{1}{2}m\left( {3600 - 900} \right)\\ &= 1350m\end{aligned}\)

Thus, it takes three times more energy to go from 30 to \(60\;{\rm{km/h}}\).