# Length contraction and time dilation atr small velocities

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1) The distance from New York to Los Angeles is about 5000 km and should take about 50 h in a car driving at 100 km/h.

a) How much shorter than 5000 km is the distance according to the car travelers?

b) How much less than 50 h do they age during the trip?

https://brainmass.com/physics/velocity/length-contraction-time-dilation-small-velocities-437879

#### Solution Preview

The distance is given by:

L_car = L/gamma(v)

where L = 5000 km is the distance according to an observer at rest (the so-called proper distance), L_car is the distance according to the observer in the car and gamma(v) is the gamma factor:

gamma(v) = 1/sqrt(1 - v^2/c^2)

We thus ...

#### Solution Summary

We explain how to compute the length contraction and time dilation. At small velocities, you have to deal with numerical errors, an expansion of the gamma factor must be used.

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