Problems Week 10
1. A particle follows the worldline ¯R = ¯R(τ). Is
d2 ¯R
dτ2
+ α2 ¯R = 0
a reasonable equation of motion (α is real and non-zero)?
2. Integrate the equation
d ¯A
dτ
= α2
ˆv
to find the most general form of the worldline that satisfies it.
3. Suppose that a spaceship moves along the worldline (in a 2-plane)
( ¯R − ¯R0)2
=
1
α2
,
with α a constant. Relate the proper time on the spaceship τ to that
of an unaccelerated observer.
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