AP Calculus AB and BC glossary
Acceleration
Acceleration is the derivative of velocity with respect to time, and therefore the second derivative of position. Comparing its sign with the sign of velocity tells you whether the object is speeding up or slowing down.
The rule for speed is about agreement of signs, not the sign of acceleration alone. When velocity and acceleration share a sign the object speeds up; when the signs differ it slows down.
The mistake
Concluding that negative acceleration means slowing down. A particle with velocity and acceleration is speeding up, because it is moving in the negative direction faster and faster.
Appears in: Unit 4: Contextual Applications, Unit 8: Applications of Integration