AP Calculus AB and BC glossary
Position function
A position function gives an object's location as a function of time. Its derivative is velocity, and the difference between two of its values is the displacement over that interval, which is why the Fundamental Theorem connects the two descriptions.
Recovering position from velocity needs an initial condition. Integrating gives position up to a constant, and a value such as pins down which antiderivative is the real one.
The mistake
Assuming position is greatest when velocity is greatest. Position peaks where velocity is zero and changing from positive to negative, not where velocity is large.
Appears in: Unit 4: Contextual Applications, Unit 8: Applications of Integration