Velocity-time graph
Also called v-t graph
A velocity-time graph plots velocity on the vertical axis against time on the horizontal. Its slope at any point gives the acceleration, and the signed area between the curve and the time axis gives the displacement.
Two readings carry almost every question asked about one.
- Slope is acceleration. The slope of the line tangent to the curve at a point is the instantaneous acceleration there, per EK 1.3.A.4.ii. A horizontal line means no acceleration at all.
- Signed area is displacement. The area bounded by the curve and the time axis over an interval equals the displacement in that interval, per EK 1.3.A.4.iii.
Signed is the word that costs the mark. Area below the axis counts negative and cancels area above it, so a trip spent equally at m/s and m/s has zero displacement. Add the same areas as unsigned magnitudes and you get the distance traveled instead. A curve crossing the axis marks the instant the object reverses; a curve that touches zero without crossing marks a pause.
The readings change on a position-time graph, which is the near-duplicate students confuse it with: there the tangent slope is the instantaneous velocity (EK 1.3.A.4.i) and the area underneath means nothing. On an acceleration-time graph the area is the change in velocity.
Straight sloped lines are constant acceleration, where the kinematic equations apply. A curved velocity-time graph is nonuniform acceleration, which an AP Physics 1 boundary statement under topic 1.3 keeps qualitative: sketch it and describe it, do not compute it.