Answer
a. 0.866c.
b. 0.986c.
Work Step by Step
The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$.
The relativistic kinetic energy is $(\gamma-1)mc^2$.
a. 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. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=6.00$
$$v=c\sqrt{1-1/\gamma^2}=0.986c$$
