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I knew that Calculus would come in handy some day.

The TRUE FACT of the matter is that at TDC and BDC, for that instant where the piston is at the maximum distance either up or down, velocity is ZERO.

Acceleration is maximum at those points.

Sorry Dogdays, Your Dog wrong. The Port velocity at those points is never ZERO, unless the engine is stationary. Unless you meant piston velocity.

Further, acceleration is minimal at those points.