The kinetic energy of an object of mass,m mov | vedclass

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Question

(D) The expression for kinetic energy is $E_k = 1/2 mv^2$.Given that the initial kinetic energy $E_k = 25\, J$ at a velocity $v = 5\, m\, s^{-1}$.$(i)

Vedclass · Accepted Answer

$100\, J, 225\, J$

Vedclass · Answer

(D) The expression for kinetic energy is $E_k = 1/2 mv^2$.Given that the initial kinetic energy $E_k = 25\, J$ at a velocity $v = 5\, m\, s^{-1}$.$(i)$ When the velocity is doubled,the new velocity becomes $v' = 2v = 10\, m\, s^{-1}$.Since $E_k \propto v^2$,the new kinetic energy $E_k' = 1/2 m(2v)^2 = 4 	imes (1/2 mv^2) = 4 	imes 25\, J = 100\, J$.$(ii)$ When the velocity is increased three times,the new velocity becomes $v'' = 3v = 15\, m\, s^{-1}$.Similarly,the new kinetic energy $E_k'' = 1/2 m(3v)^2 = 9 	imes (1/2 mv^2) = 9 	imes 25\, J = 225\, J$.

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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