Q21 A car moves at a constant speed of 150 miles per hour in

Q2.1 A car moves at a constant speed of 150 miles per hour in a straight line on the autobahn. There are timing devices embedded in the road at two locations that record the times at which cars pass them. The data from the timing devices shows that it took 10 minutes to pass between them. How much time would have passed on the dashboard clock (a clock at rest with respect to the car) as it drove between the two timing locations? The difference between the two times is so small that your calculator may not properly resolve it. Check it by calculating the difference between the road and dashboard times using the approximation (1 + x)a 1 + ax, for |x| 1.

Solution

t time on the ground and t’ is the time interval recorded by the dashboard clock between the event, then we will have

t = t’/(1-v²/c²)

Speed of the car = 150 mph

                              = 241.35 kmph

                              =67.05 m/s

V²/c² = 67.05/3x10⁸

           = 22.35 e-8

Dash board recorded time interval

t’ = t (1-v²/c²)

        = t (1-0.5*22.35x10^-8)   minutes

The difference between the two clocks

               = 11.18e-8 minutes

               =6.7e-6 s

The dash board clock will read 6.7e-6 secs less than that on the road.