Answer
a.$v=0.140c$.
b. $v=0.417c$.
c. $v=0.866c$.
Work Step by Step
The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$.
a. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=1.010$
$$v=c\sqrt{1-1/\gamma^2}=0.140c$$
b. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=1.10$
$$v=c\sqrt{1-1/\gamma^2}=0.417c$$
c. Solve for v when $\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=2.00$
$$v=c\sqrt{1-1/\gamma^2}=0.866c$$
