## Relativity: Proper time and length

(a) Write down the definition of proper time and explain how to use the appropriate formula with an example.

(b) Write down the definition of proper length and explain how to use the appropriate formula with an example.

(c) At what relative speed does a clock move if it runs at a rate that is one-half the rate of a clock at rest?

(d) At what relative speed does a meter stick move if its length is observed to shrink to 0.25 m?

(e) Two spaceships approach each other, each moving with the same speed as measured by a stationary observer on the Earth. Their relative speed is 0.70c. Determine the velocities of each spaceship as measured by the stationary observer on Earth.

i know that proper time/length means it's the time of an observer's own measurement, but how would you describe that using formulas?

Sorry but i really couldn't find any website/books with a good explanation. Thanks guys
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 All you'll have to understand is that the term is "proper time-interval" not "proper time". the proper time interval is the time interval observed in a reference frame in which the two events that determines the time interval occurs in the same place. the proper length is the length measured in a reference frame with respect to which, the object whose length is to be measured, is at rest. If you still don't understand, look up in Halliday/Resnick/Walker. it's helpful.

 Tags clock, length, proper time, relativity

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