Exam-style question
Try this first
Which equation correctly expresses proper time in terms of coordinate time and relative velocity?.
- A.Δτ = Δt √(1 – v²/c²)
- B.Δτ = Δt / √(1 – v²/c²)
- C.Δτ = Δt (1 – v²/c²)
- D.Δτ = Δt + v²/c²
Model answer
What a good answer should say
- Δτ = Δt √(1 – v²/c²)
Explanation
Why this works
Formula/rule: Δτ = Δt / γ = Δt √(1 – v²/c²). Substitution: For a clock moving at v = 0.8c, γ = 1/√(1 – 0.64) = 1.666…, so Δτ = Δt / 1.666… = 0.6 Δt.
Working: Δτ = Δt √(1 – 0.64) = Δt √0.36 = 0.6 Δt. Answer: proper time is less than coordinate time for a moving clock.
Units/conclusion: proper time is measured in seconds.
Common mistake
No common mistake is linked to this question yet.