Question

When the speed of a moving object is doubled, its

• A. acceleration is doubled
• B. weight is doubled
• C. K.E. is doubled
• D. K.E. becomes $4$ times

Answer 1

The correct option is D

K.E. becomes $4$ times

Step 1: Given data

The speed of a moving object is double. So, if the initial speed is $v$ and the final speed is $v\text{'}$, then

$v\text{'}=2v$

Step 2: Finding kinetic energy

A moving object possesses kinetic energy by virtue of its motion.

The kinetic energy (K.E.) of a body of mass $m$ moving with speed $v$ is given by

$K.E.=\frac{1}{2}m{v}^2$

When the speed is doubled, the kinetic energy of the body becomes

$$\begin{gathered} K.E.\text{'}=\frac{1}{2}mv{\text{'}}^2 \\ =\frac{1}{2}m{\left(2v\right)}^2 \\ =4·\frac{1}{2}m{v}^2 \\ =4K.E. \end{gathered}$$

Thus, when the speed of an object is doubled, its kinetic energy becomes $4$ times its initial kinetic energy.

Hence, option D is correct.