A stationary observer Bob, observes Alice take 5 seconds to travel from point A to B at 0.95c. How much time does Alice measure the journey from A to B to take?

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This question is all about the application of Special Relativity. 

In order to solve this problem we need to identify that the correct equation to use here is:

t= (gamma factor)t0

Where t is the time observed by Bob, t0 is the time observed by Alice and the gamma factor = 1/Sqrt(1-(v2/c2)

We need to rearrange the equation for t0, giving 

t0=t/(gamma factor) 

t0= t(Sqrt(1-(v2/c2))

Subsituting t =5 s, v = 0.95c, we obtain:

t0=(5 s)(Sqrt(1-0.952))

t0 = 1.56 s

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