An object of mass $2\ \mathrm{kg}$ has a linear momentum of magnitude $6\ \mathrm{kg \cdot \displaystyle \frac{m}{s}}$. What is this object’s kinetic energy?
A) $3\ \mathrm{J}$
B) $6\ \mathrm{J}$
C) $9\ \mathrm{J}$
D) $12\ \mathrm{J}$
A) $3\ \mathrm{J}$
B) $6\ \mathrm{J}$
C) $9\ \mathrm{J}$
D) $12\ \mathrm{J}$
The magnitude of the object’s linear momentum is
$$p=mv$$
If $p=6\ \mathrm{kg \cdot \displaystyle \frac{m}{s}}$ and $m=2\ \mathrm{kg}$ then
$$v=3\ \mathrm{\displaystyle \frac{m}{s}}$$
Therefore, the object’s kinetic energy is
$$K=\frac{1}{2}mv^2$$
$$K=(2\ \mathrm{kg})\left(3\ \mathrm{\displaystyle \frac{m}{s}}\right)^2$$
$$K=9\ \mathrm{J}$$