Displacement

Also called Change in position

Displacement is the vector change in an object's position, measured straight from the starting point to the ending point. It has both magnitude and direction, does not depend on the route taken, and is zero for any trip that ends where it began.

Symbol Δx\Delta x in one dimension, Δr\Delta \vec{r} in two or three. The SI unit is the meter. The defining equation is final position minus initial position, Δx=xx0\Delta x = x - x_0, so in one dimension the sign carries the entire direction: positive means the object finished on the positive side of where it started.

Only the endpoints matter. Run one lap of a 400 m track and you cover 400 m of distance, but your displacement is zero, because the finish line is the start line. Distance accumulates along the path; displacement does not know the path exists. That is the split that costs marks, and it is why average speed and the magnitude of average velocity come out as different numbers for the same trip.

Displacement is a vector and distance is a scalar; the AP Physics 1 CED puts both on that list in EK 1.1.A.3. On a velocity-time graph the signed area between the curve and the time axis gives displacement, so area below the axis subtracts rather than adds.

Topic 1.2 Displacement, Velocity, and Acceleration carries the AP framing, and the kinematic equations guide is where you solve for it.

Back to the physics glossary