Calculus and Usain Bolt

The link is to a 'Science and Technology' article about a guy who ran in the recent Olympics.

Yes, and some very elementary math.

Fuzzy even.

How at t=0 is his distance traveled = 0 (this sounds right), but his velocity is 2 m/s and his acceleration is 6 m/s2.

Seems like they should all start at 0 to me...or maybe I was taught a "different" type of calculus.

The first chart is looks good. But the (3) charts below it, the acceleration chart look like an instantaneous start or a running start beforehand and I agree with the velocity chart, unless he had a running start also.

I hadn't looked at it that closely. The velocity at t=0 should be 0, but it would jump very quickly from there. The chart that shows v=2 at t=0 is from an equation fitted to the data, apparently not fitted very well!

It looks like they curve fitted the distance versus time at 10 meter intervals, took the derivative to get speed and the derivative of speed to get acceleration. Integration tends to reduce "noise" whereas taking the derivative increases it. Given the number of data points, the velocity and particularly the acceleration will not be very accurate.

Bolt is pretty impressive. He can run faster than I can ride a bike...

Our coaches used to say that sprints were won and lost in the starting blocks. Some of that is true here, considering narrow margins of some victories over the years. The calculus shown did not work, because improper boundary values were chosen for the differential equations. Too bad. Start over, and do it right.

And to think that these guys wrote a textbook ...

They took ten samples, made an approximation curve, and then differentiated the formula of the approximation twice to get velocity and acceleration.

The approximation curve should have been constrained to include velocity at time zero is zero (zero slope at zero).

And once again overly complicating something leads to an incorrect result.

If I wanted to know how fast he was I would have just timed him between two fixed physical points.

Oh wait. Never mind. The geniuses that set up the event for the Olympics already did that and also know exactly how fast he is as well.

Clever bastards using practical applied math to solve a real world problem. What were they thinking?

a practice in futility.

Actually to do this correctly, they should have used laser time of flight to record his times through the continuous 100 meters. Then the calculus would be correct as to his acceleration all the way through. Or another way: attach small accelerometers to his torso, and average out the jolts of his feet impacting the track, while mainly measuring acceleration in the forward direction only.

An athlete start with his center of gravity behind the zero distance point .

There may also be a small delay before movement starts.