📚 Part 1: Multiple Choice

1. Which best describes an inertial frame of reference?

A frame in which Newton's laws hold and objects move at constant velocity unless acted on

A frame that is accelerating relative to the Earth

Any rotating frame

A frame fixed to the surface of the Earth only

2. Which pair are Einstein's two postulates of Special Relativity?

The laws of physics are the same in all inertial frames; the speed of light in vacuum is the same in all inertial frames

The speed of light is constant only in one preferred frame; time is absolute

Energy is conserved; mass is conserved

All observers measure the same frequency for light; lengths are invariant

3. Which equation gives time dilation (t is dilated time, t₀ is proper time)?

t = t₀ √(1 - v²/c²)

t = t₀ / √(1 - v²/c²)

t = t₀ (1 - v/c)

t = t₀ (1 + v²/c²)

4. Check all items that provide experimental evidence supporting Special Relativity:

The Michelson–Morley null result

Observed muons reaching sea level with extended lifetimes

Time correction required for GPS satellites to stay accurate

Classical Galilean velocity addition working at v ≈ c

✏️ Part 2: Short Answers & Calculations

5. Time dilation calculation — muon lifetime.

Proper lifetime t₀ = 2.2 μs. Calculate the dilated lifetime t when v = 0.98c. Show working. Use γ = 1 / √(1 − v²/c²).

6. Length contraction calculation.

A rod has proper length l₀ = 10.0 m. Find its length l as measured by an observer if the rod moves past at v = 0.60c. Show working.

7. Energy concepts — short answer.

Write one clear sentence distinguishing rest energy (E₀) from total relativistic energy (E). You may use E₀ = m₀c².

8. Bertozzi & classical vs relativistic KE.

In 2–3 sentences, explain why Bertozzi's experiment shows the classical kinetic energy formula fails at high speeds and how relativity resolves this.

🧩 Part 3: Matching & Concept Checks

9. Match each term (left) with the correct definition (right). Draw lines between columns.

A. Proper time (t₀)

B. Dilated time (t)

C. Proper length (l₀)

D. Lorentz factor (γ)

1. Time measured in the rest frame of the moving clock

2. Time interval measured by a stationary observer for a moving clock (longer)

3. γ = 1 / √(1 − v²/c²)

4. Length measured in the object's rest frame

10. Quick conceptual check — one line:

Why can no massive object be accelerated to v = c? Write a single concise reason.

Special Relativity Practice

Special Relativity Practice

📚 Part 1: Multiple Choice

✏️ Part 2: Short Answers & Calculations

🧩 Part 3: Matching & Concept Checks

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