Answer
a. v = 0.866c.
b. v = 0.608c.
Work Step by Step
a. The momentum is $\gamma mv$.
The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$.
Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=2.00$
$$v=c\sqrt{1-1/\gamma^2}=0.866c$$
b. According to equation 37.32, in this situation, the force is $F=\gamma^3 ma$.
Solve for v when $\gamma^3=2.00$
$$\gamma=2.00^{1/3}$$
$$v=c\sqrt{1-1/\gamma^2}=0.608c$$
