Question

An object has a kinetic energy of 175 J and a momentum of magnitude 25.0 kg m/s. Find the speed of the object.

Answer 1

Let denotes the kinetic energy of the object is $K$ , momentum is $p$ and mass is $m.$

We know that,

$$K=\frac{1}{2}mv^2 \hspace{1cm}(1)\\ p=mv\hspace{1cm} (2)$$

We have given that,

$$K=175J\\ p=25.0kg\:ms^{-1}$$

Now. divide the equation $(1)$ by $(2)$ we get,

$$\frac{K}{p}=\frac{\frac{1}{2}mv^2}{mv}\\ \implies \frac{2K}{p}=v \hspace{1cm}(3)$$

Thus, from equation $(3)$ we get speed of the object is

$$v=\frac{2\times 175}{25}=14ms^{-1}$$

Hence, we are done.