A certain automobile is 6.0 m long if at rest.If it is measured to be 4.8 m long while moving, its speed is:
A)0.1c
B)0.3c
C)0.6c
D)0.8c
E) 0.95c

Question

A certain automobile is 6.0 m long if at rest.If it is measured to be 4.8 m long while moving, its speed is:
A)0.1c
B)0.3c
C)0.6c
D)0.8c
E)> 0.95c

Quizplus · Accepted Answer

This is a special case of length contraction in relativity theory. The formula for length contraction is given by L' = L√(1 - v^2/c^2), where L is the rest length, L' is the length when moving at velocity v, and c is the speed of light. Plugging in the given values, we have:

4.8 = 6√(1 - v^2/c^2)

Squaring both sides and simplifying, we get:

v^2/c^2 = 1 - (4.8/6)^2
v^2/c^2 = 1 - 0.2^2
v^2/c^2 = 0.96
v/c = ±0.9798

The negative solution corresponds to the car moving backwards, so we take the positive solution:

v/c = 0.9798
v = 0.9798c

Therefore, the best choice is (C) 0.6c.

A Certain Automobile Is 6