AP Calculus AB and BC glossary
Rectilinear motion
Also called: Motion along a line
Rectilinear motion is movement along a straight line. Position differentiates to velocity, velocity differentiates to acceleration, and integrating runs the chain backwards, which is why one motion problem can test both halves of the course.
The particle changes direction where velocity changes sign, not where acceleration does. Speed increases when velocity and acceleration share a sign, which is the most commonly tested subtlety in the topic.
The mistake
Confusing displacement with total distance. Displacement integrates velocity; total distance integrates the absolute value of velocity, and they differ whenever the particle turns around.
Appears in: Unit 4: Contextual Applications, Unit 8: Applications of Integration