A car is moving to the left with speed 05 c At t0s you measu

A car is moving to the left with speed 0.5 c. At t=0s, you measure the length of the car by taking note the position of the front end (x2=-6m) and the back end(x1=0m). What are the coordinates of these two points in the car frame?

Solution

Coordinates of the points in the car frame is proper length Lp

      L = L_p / sqrt ( 1 - v² /c ² )

       6 m = L_p / sqrt ( 1 - (0.5c)² /c² )

         L _p =5.196 m

so the coordinates are -5.196 m from the origin.