Use the graph of Lorentz factor γ versus v/c. A probe passes Earth at 0.90c; its onboard clock measures 2.0 s between beacon flashes. What interval does Earth measure?

Use the γ versus v/c graph. A ship moving at 0.60c records 8.0 s of proper time between two engine pulses. What time interval does a station observer measure?

Use the γ versus v/c graph. A moving particle's own clock measures 3.0 ms between two flashes while it travels at 0.80c. What interval is measured in the lab?

Use the γ versus v/c graph. A muon traveling at 0.99c has a proper lifetime of 1.5 µs in its own frame. What lifetime does an Earth observer measure?

Use the γ versus v/c graph. A spacecraft clock measures 0.50 s between two beeps while the craft moves at 0.95c. What interval does Earth measure?

Use the γ versus v/c graph. A fast probe at 0.40c records 12 s between two onboard events. What interval does an observer at rest with Earth measure?

A spacecraft travels at 0.60c. Its clock measures 4.0 s between launch and landing of a ball at the same spot in the cabin. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What does the station measure?

A particle moves through a lab at 0.80c. Its own clock measures 6.0 µs between two decays in a detector it carries. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What interval does the lab measure?

A rocket passes Earth at 0.90c. A clock on the rocket measures 5.0 s between two flashes from the same onboard lamp. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What does Earth measure?

A moving clock travels at 0.50c, and its proper time between two ticks is 20 ns. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What time between ticks is measured by a stationary observer?

A spacecraft clock measures 30 s while passing a beacon at 0.70c. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What interval does the beacon's inertial frame measure?

A capsule moves at 0.95c. Its onboard timer reads 2.0 s between two radio pulses from the same antenna. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What interval does Earth measure?

An ion moves at 0.30c. In the ion's rest frame, two events are separated by 100 ns. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What interval is measured in the lab?

A muon travels at 0.99c. Its proper lifetime is 2.2 µs. Use $\gamma =\frac{1}{\sqrt{1-v^2/c^2}}$. What lifetime does an Earth observer measure?

A spacecraft antenna emits two pulses from the same point on the craft. Which clock measures the proper time between the emissions?

Two sparks occur at the same marked point on a lab bench while a rocket flies by. Who measures the proper time between the sparks?

A muon is created and later decays while moving through the atmosphere. Which observer would measure the muon's proper lifetime?

A passenger taps the same spot on a train seat twice as the train passes a platform. Which clock measures the proper time between taps?

A ground detector records two particle hits at the same sensor while a spacecraft passes overhead. Which frame measures the proper time between the hits?

An astronaut starts and stops a wristwatch timer while holding it in the same hand. Which time is the proper time for those start and stop events?

An airliner travels at about 250 m/s, roughly 0.0000008c. Why do its clocks differ from airport clocks by only tiny amounts after a flight?

A car moves at 30 m/s, about 0.0000001c. What does special relativity predict about time dilation for the car's clock?

Cosmic-ray muons created high in the atmosphere can reach the ground even though their rest lifetime is short. What explains this in Earth's frame?

A lab finds that unstable particles moving at high speed last longer in the lab than identical particles at rest. Which interpretation matches special relativity?

A student says time dilation only means light from a moving clock arrives late. What is the best correction?