Motion in a Straight Line
Acceleration and motion graphs
Read the signs and sizes of x, v and a from x-t, v-t and speed-time graphs.
Acceleration is the rate of change of velocity. Average acceleration = Δv/Δt; instantaneous acceleration a = dv/dt, the slope of the v–t graph. Its SI unit is m s⁻².
Each graph tells you something through its slope or its area:
| Graph | Its slope gives | The area under it gives |
|---|---|---|
| x–t | velocity | nothing useful |
| v–t | acceleration | displacement |
| a–t | (not used here) | change in velocity |
On an x–t graph, a straight line means steady velocity (a = 0); a line that curves upward means a > 0; one that curves downward means a < 0. The area under a v–t graph is a displacement because height (m s⁻¹) × base (s) gives metres.
The sign of a alone does not tell you whether a body speeds up. It speeds up when a and v have the same sign, and slows down when their signs differ. A car reversing (v negative) while the driver brakes (a positive) is slowing down.
Zero velocity does not mean zero acceleration. A ball thrown straight up stops for an instant at the top (v = 0), but gravity is still pulling, so a = g there.
Some graphs can never happen, because they break the rules of real motion:
- A vertical line on an x–t graph: time standing still.
- A body in two places at the same instant.
- A speed that is negative, or a path length that decreases: both only ever grow or stay the same.
Practise this lesson
Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.
No account, no email address. Opens the real product.