A classical mechanics problem by Matthew Carmichael

Jill works as a director of traffic at roadworks, with a Stop-Go flip sign. Fed up of counting cars, she wants a better way to know when she should flip her sign to Go.

She realizes all she needs is a stopwatch and to watch 1 car.

She witnesses the final car going past her (through the roadworks towards her friend) and instantly flips her sign to Stop, and starts the stopwatch, preventing traffic from passing her.

Her friend, Fred, working at the other end (100m away from Jill) allows 10 cars to pass through (towards Jill), which all average 20 mph. Assuming that the cars all stick to the Highway code and are exactly 2 seconds apart, how many seconds is it before Jill flips her sign to go?

Assumptions: Each car has negligible length (effectively a point source) (0m)


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