A relativistic car is 4.5 m in length. The car is measured to be 4.0 m in length when it speeds at a velocity of

Question

Quizplus · Accepted Answer

The length contraction formula is $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the contracted length, $L_0$ is the rest length, $v$ is the velocity, and $c$ is the speed of light. Rearranging for $v/c$, we get $v/c = \sqrt{1 - (L/L_0)^2}$. Plugging in $L = 4.0$ m and $L_0 = 4.5$ m, we find $v/c \approx 0.46$, corresponding to choice B.

A Relativistic Car Is 4