Make a graph of the kinetic energy versus momentum for a particle of nonzero rest mass

If you were to travel to a star 125 light-years from Earth at a speed of $2.50 \times 10^{8} \mathrm{m} / \mathrm{s},$ what would you measure this distance to be?

Two protons, each having a speed of $0.990 c$ in the laboratory, are moving toward each other. Determine the momentum of one proton as seen by the other proton.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 0.999 c

Two protons, each having a speed of $0.990 c$ in the laboratory, are moving toward each other. Determine the total momentum of the two protons in the laboratory.

Two protons, each having a speed of $0.990 c$ in the laboratory, are moving toward each other. Determine the momentum of each proton in the laboratory.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 0.98 c.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 0.95 c.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 0.200 c.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 0.020 c.

Lengths and time intervals depend on the factor $\sqrt{1-v^{2} / c^{2}}$ according to the theory of relativity. Evaluate this factor for speeds of: v = 20,000 m/s (typical speed of a satellite).

What magnetic field intensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \mathrm{GeV} / \mathrm{c}^{2},\left(1 \mathrm{GeV}=10^{9} \mathrm{eV} .\right)$ [Hint: in relativity, it is still true that $m v^{2} / r=q v B$ in a magnetic field.]

Calculate the kinetic energy and momentum of a proton $\left(m_{0}=1.67 \times 10^{-27} \mathrm{kg}\right)$ traveling $7.35 \times 10^{7} \mathrm{m} / \mathrm{s}$. By what percentages would your calculations have been in error if you had used classical formulas?

An electron $\left(m=9.11 \times 10^{-31} \mathrm{~kg}\right)$ is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.20 \times 10^{-14} \mathrm{~J}$. Determine the electron's speed, $v$.