#### Answer

a. $\sqrt{3}$.
b. $\frac{1}{4}$.

#### Work Step by Step

a. Use equation 6–3 for the kinetic energy and solve for the speed.
$$KE = \frac{1}{2} mv^{2}$$
$$v=\sqrt{\frac{2 \times KE}{m}} $$
The speed is proportional to the square root of the KE. If the kinetic energy is tripled, the speed changes by a factor of $\sqrt{3}$.
b. The KE is proportional to the square of the speed. If the speed is halved, the kinetic energy changes by a factor of $\frac{1}{4}$.