Question

A $1\mathrm{kg}$ mass has a K.E. of $1\mathrm{J}$ when its speed is

• A. $1.4{\mathrm{ms}}^{-1}$
• B. $0.45{\mathrm{ms}}^{-1}$
• C. $4.4{\mathrm{ms}}^{-1}$
• D. none of these

Answer 1

The correct option is A

$1.4{\mathrm{ms}}^{-1}$

Step 1: Given data

Mass of body, $m=1\mathrm{kg}$

Kinetic energy of the body, $K.E.=1\mathrm{J}$

Step 2: Calculating the speed

The kinetic energy of a body of mass $m$ with speed $v$ is given by

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

Substituting the given values, the speed of the body is found to be

$$\begin{gathered} 1kgm{s}^{-1}=\frac{1}{2}\times 1kg\times v^{2}m{s}^{-1} \\ 2=v^2 \\ v=1.4m{s}^{-1} \end{gathered}$$

Thus, the speed of the body is $1.4{\mathrm{ms}}^{-1}$.

Hence, option A is correct.