An electron is accelerated so that its kinetic energy is greater than its rest energy $m_{0} c^{2}$ by a factor of 5.00. What is the speed of the electron in each case?

An astronaut on a spaceship traveling at $0.75 c$ relative to Earth measures his ship to be $23 \mathrm{~m}$ long. On the ship, he eats his lunch in $28 \mathrm{~min}$. How long does the astronaut's lunch take to eat according to observers on Earth?

Two protons, each having a speed of 0.935c in the laboratory, are moving toward each other. Determine the momentum of one proton as seen by the other proton.

When two moles of hydrogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reaction? What % of the total original mass of the system does this mass change represent?

An astronaut on a spaceship traveling at $0.75 c$ relative to Earth measures his ship to be $23 \mathrm{~m}$ long. On the ship, he eats his lunch in $28 \mathrm{~min}$. What length is the spaceship according to observers on Earth?

Two protons, each having a speed of 0.935c 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 0.935c in the laboratory, are moving toward each other. Determine the momentum of each proton in the laboratory.

Suppose a $14,500 \mathrm{~kg}$ spaceship left Earth at a speed of $0.90 c$. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (about $10^{20} \mathrm{~J}$ ).

What is the percentage increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.]

A $36,000 \mathrm{~kg}$ spaceship is to travel to the vicinity of a star $6.6$ light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than $1.0$ year. How much work must be done on the spaceship to bring it to the speed necessary for this trip?

In an Earth reference frame, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years?

In a nuclear reaction two identical particles are created, traveling in opposite directions. If the speed of each particle is $0.82 c$, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle?

Show analytically that a particle with momentum p and energy E has a speed given by $v=\frac{p c^{2}}{E}=\frac{p c}{\sqrt{m_{0}^{2} c^{2}+p^{2}}}$

A spaceship and its occupants have a total mass of $160,000 \mathrm{~kg}$. The occupants would like to travel to a star that is $35$ light-years away at a speed of $0.70 c$. To accelerate, the engine of the spaceship changes mass directly to energy. Assuming the acceleration is rapid, so the speed for the entire trip can be taken to be $0.70 c$, determine how long the trip will take according to the astronauts on board.