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Just for fun, I looked up some values for the following engines for comparison: F1, NASCAR, Honda CBR 600RR, and Honda K20.  F1 used to spin 20k rpms and NASCAR used to hit 10k, but I used their current limits of 18k and 9k in this comparison.    It’s interesting to see that the 600cc motorcycle engine actually has the lowest piston velocity at its redline rpm.  All of their maximum velocities are relatively close though.  Check out the differences in acceleration!  The short strokes of the F1 and 600c engines keep the piston speeds low, but accelerations can’t hide.  Making pistons go back and forth that quickly results in really high accelerations.

Let’s say you’re like Rockwood and me and haven’t had calculus in over a decade and the identity for taking the derivative of the square root of sin squared eludes you.  One thing you can do is to calculate the changes in velocity and acceleration in really small increments.  Going back to the 40 yard dash, we calculated an average speed of 0.8 yards/second by dividing the change in distance (40 yards) by the time it took to travel it (5 seconds).  Did the runner instantly start at 0.8 yards/second?  Nope.  Was the acceleration of the runner constant?  Nope.  But because we only had the time measurement after a change of 40 yards, our values are pretty far off from reality if we wanted to know the exact speed and acceleration at 5 yards or 10 yards.  If we knew the time of the runner at 1 yard increments, we could plot the velocity and acceleration of the runner much more accurately.