Question

2) By what factor does an object's kinetic energy change if its speed is doubled? By what factor does its momentum change?

Answer 1

Let the object has mass m and speed v initially.

Then, kinetic energy will be

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

and the momentum will be

$p=mv$

Now, if the speed is doubled, v'=2v

then kinetic energy will be

$\begin{gathered} K\mathrm{}E\mathrm{}^{\prime}=\frac{1}{2}m\times4v^2 \\ =4\times K.E. \end{gathered}$

Also, momentum will be

$\begin{gathered} p^{\prime}=m\times2v \\ =2p \end{gathered}$

Hence, kinetic energy changes by a factor of 4 and momentum changes by a factor of 2 when speed is doubled.