displacement

Meaning: Displacement is a vector pointing from an object's initial position to its final position. Its magnitude is the straight-line separation of the two points, and it depends only on the endpoints, not on the path. Distance traveled is a scalar equal to the total path length. In general chemistry, a displacement reaction is a different idea: one element replaces another in a compound.

Equation: Δx = xf − xi, where Δx is displacement (m), xf is final position (m), and xi is initial position (m). In two dimensions, Δr = rf − ri, and the components are handled separately.

On the MCAT: Expect a multi-leg or round trip where you add vectors, often with the Pythagorean theorem, to find net displacement. On a velocity–time graph, the signed area under the curve is displacement, whereas distance requires adding the areas without regard to sign. Under constant acceleration, Δx = v₀t + ½at².

Common confusion: Students treat displacement and distance as the same thing. Their magnitudes match only for motion in a straight line with no reversal. A runner who completes one lap returns to the start, so displacement is zero and average velocity is zero, but the distance and average speed are not zero.