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Date November 2016 Marks available 1 Reference code 16N.3.SL.TZ0.7
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Draw Question number 7 Adapted from N/A

Question

Identical twins, A and B, are initially on Earth. Twin A remains on Earth while twin B leaves the Earth at a speed of 0.6c for a return journey to a point three light years from Earth.

Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.

[1]
a.

Determine the time taken for the journey in the reference frame of twin B.

[2]
b.

Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for both twins.

[1]
c.

Suggest how the twin paradox arises and how it is resolved.

[2]
d.

Markscheme

«0.6 ct = 6 ly» so t = 10 «years»

 Accept: If the 6 ly are considered to be measured from B, then the answer is 12.5 years.

a.

ALTERNATIVE 1

10− 6t2 − 02

so t is 8 «years»
Accept: If the 6 ly are considered to be measured from B, then the answer is 10 years.

ALTERNATIVE 2

gamma is \(\frac{5}{4}\)

10 × \(\frac{4}{5}\) = 8 «years»

Allow ECF from a
Allow ECF for incorrect γ in mp1

b.

three world lines as shown

Award mark only if axes OR world lines are labelled.

c.

according to both twins, it is the other one who is moving fast therefore clock should run slow

Allow explanation in terms of spacetime diagram.

«it is not considered a paradox as» twin B is not always in the same inertial frame of reference

OR

twin B is actually accelerating «and decelerating»

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.3 – Spacetime diagrams
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