AP Calculus AB and BC glossary

Displacement

Displacement is the net change in position over a time interval, found by integrating velocity. It is signed, so a round trip that returns to the start has a displacement of zero no matter how far the object travelled.

displacement=∫abv(t) dt,distance=∫ab∣v(t)∣ dt\text{displacement} = \int_a^b v(t)\,dt, \qquad \text{distance} = \int_a^b |v(t)|\,dt

Displacement is a change, not a location. To report where an object ends up, add the displacement to the starting position: the final position is the initial position plus the integral of velocity over the interval.

The mistake

Reporting displacement when the question asks for distance travelled. If the velocity changes sign anywhere on the interval, the two answers differ.

Physics makes the same separation between displacement and distance, and marks displacement as the vector of the pair: displacement.

Appears in: Unit 8: Applications of Integration