Calculate the speed of a lion with kinetic energy 137 J and mass 76 kg (give the speed to 3 signific

What you are being asked to find

You are given the kinetic energy and mass, and you need the speed. Kinetic energy depends on speed squared, so we rearrange the kinetic energy formula and then substitute the numbers.

Start with the kinetic energy equation

$$E_k = \tfrac{1}{2}mv^2$$ Rearrange to make $v$ the subject: $$v^2 = \frac{2E_k}{m} \quad\Rightarrow\quad v = \sqrt{\frac{2E_k}{m}}$$

Substitute values and calculate

Substitute $E_k = 137\ \text{J}$ and $m = 76\ \text{kg}$: $$v = \sqrt{\frac{2(137)}{76}} = \sqrt{\frac{274}{76}} = \sqrt{3.605263\ldots} = 1.898\ldots\ \text{m/s}$$ Rounded to 3 significant figures: $$v = 1.90\ \text{m/s}$$

Quick units check

A joule is $\text{kg}\,\text{m}^2\text{s}^{-2}$, so $\frac{2E_k}{m}$ has units $\text{m}^2\text{s}^{-2}$. Taking the square root gives $\text{m/s}$, which matches a speed.