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Time Dilation: Public Worked Question

A public special-relativity question showing how to identify the proper time and apply the Lorentz factor to a moving clock.

Question

A starship travels at v=0.6cv = 0.6c relative to Earth. The crew measures 8.0 s8.0\,\text{s} between two ticks of a clock on board. How much time elapses between those same two ticks as measured by Earth observers?

  1. a.12.5 s12.5\,\text{s}
  2. b.10 s10\,\text{s}
  3. c.8.0 s8.0\,\text{s}
  4. d.6.4 s6.4\,\text{s}

Correct answer

B. 10 s10\,\text{s}

Full reasoning

  1. 1The crew's 8.0 s8.0\,\text{s} is the proper time Δτ\Delta\tau, because both ticks occur at the clock's own location in the ship frame.
  2. 2Compute the Lorentz factor: γ=1/1−(0.6)2=1/0.64=1/0.8=1.25\gamma = 1/\sqrt{1 - (0.6)^2} = 1/\sqrt{0.64} = 1/0.8 = 1.25.
  3. 3Earth observers measure the dilated interval Δt=γΔτ=1.25×8.0=10 s\Delta t = \gamma\Delta\tau = 1.25 \times 8.0 = 10\,\text{s}.

Why each choice is right or wrong

Choice A

This uses γ=1/(1−v2/c2)=1/0.64=1.5625\gamma = 1/(1 - v^2/c^2) = 1/0.64 = 1.5625 without taking the square root in the denominator.

Choice B

Correct. γ=1/1−0.36=1/0.8=1.25\gamma = 1/\sqrt{1 - 0.36} = 1/0.8 = 1.25, and the dilated interval is 1.25×8.0=10 s1.25 \times 8.0 = 10\,\text{s}.

Choice C

This assumes both frames share a universal time; in special relativity the moving clock's interval is dilated for Earth observers.

Choice D

This divides by γ\gamma instead of multiplying, which would make the moving clock appear to run fast rather than slow.

Related formula

Time dilation

Δt=γΔτ,γ=11−v2/c2\Delta t = \gamma\Delta\tau,\quad \gamma = \frac{1}{\sqrt{1 - v^2/c^2}}

Assumptions: Both frames are inertial. The proper-time clock is present at both events.

Related topic and practice

Special Relativity EssentialsSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 3, Section 5.3: Time Dilation — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
Publisher record
Keiko Study editorial owner
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Reviewer record
Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

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