The Last 100m Sprint (supposedly)-XC

This is a picture of me approaching the finish line at the Kamehameha Invitational last Saturday. After learning about momentum and impulse this week, I realized that these concepts closely tie into the finish of a cross-country race. My understanding of momentum and impulse from physics has helped me to understand why my coach tells everyone to run THROUGH the finish line (as opposed to stopping at the finish line). Impulse is equal to the change in momentum and the average force*elapsed time. Momentum is mass*velocity, so the change in my momentum at the finish is equal to -my mass*my sprinting speed because if I stop completely at the end my final velocity is 0. The value for change in momentum should be equal to average force*elapsed time, since both expressions are equivalent to impulse. Because the change in momentum is not 0, the equation requires that the elapsed time cannot be zero either. Therefore, since I am changing my momentum at the finish line, I must take time to slow down to rest; I cannot stop instantaneously. Because I have to slow down over a period of time to make the change in momentum, I would have to start decreasing my speed before the finish line in order to stop at the finish line. This would mean that I cannot run at sprinting speed for the whole 100m stretch, hence a slower time and getting passed by other runners right at the finish line. By following the coach's advice and running THROUGH the finish line, I will start reducing my speed after I cross the finish line, so I will be able to run the entire last 100m at top speed (and hopefully pass other runners who aren't thinking about the physics behind their race finish).