AP Calculus AB and BC glossary
Velocity
Velocity is the derivative of position with respect to time. It is a signed quantity, so its sign tells you the direction of motion, and its absolute value is the speed.
Positive velocity means motion in the positive direction and negative velocity means motion in the negative direction. A particle is momentarily at rest when velocity equals zero, which is also where it may change direction.
Integrating velocity over an interval gives displacement, the net change in position. Integrating the absolute value of velocity gives total distance travelled, which is a different and usually larger number.
The mistake
Confusing displacement with distance. If a particle moves forward 5 and back 3, the displacement is 2 but the distance travelled is 8.
Appears in: Unit 4: Contextual Applications, Unit 8: Applications of Integration