Quiz – Special Relativity

What is the Lorentz factor for an object travelling at 0.840c?

What is the Lorentz factor for an object travelling at 1.41 x 10^8 m/s? Assume that the speed of light in a vacuum is 3.00 x 10^8 m/s.

A train with a resting length of 275 m is travelling at 0.250c relative to a stationary observer. How long will the train appear to the stationary observer? Answer in metres, using numbers only (i.e. '1.9' for an answer of 1.9 m).

A train with a resting length of 225 m is travelling very fast relative to a stationary observer. The train appears 173 m long to the stationary observer. How fast is the train moving relative to the observer, as a percentage of the speed of light? Answer using numbers only (i.e. '72.5' for an answer of 72.5% of the speed of light).

A train with a resting length of 275 m is travelling very fast relative to a stationary observer. The train appears 272 m long to the stationary observer. How fast is the train moving relative to the observer (in m/s)? Answer using numbers only (i.e. '282000000' for an answer of 2.82 x 10^8 m/s).