Displacement–time graphs
On a displacement–time (s–t) graph, the gradient equals the velocity. A horizontal line means the object is stationary; a steeper line means a higher velocity; a curve means changing velocity.
Key idea
On an s–t graph: velocity = gradient = (change in s) ÷ (change in t).
On a v–t graph: acceleration = gradient and distance = area under the graph.
Velocity–time graphs
On a velocity–time (v–t) graph, the gradient gives the acceleration and the area under the graph gives the distance travelled. A horizontal line means constant velocity (zero acceleration); a positive slope means acceleration; a negative slope means deceleration.
Worked example
A v–t graph shows velocity rising uniformly from 0 to 20 m s⁻¹ in 4 s, then staying at 20 m s⁻¹ for 6 s.
Acceleration in the first stage = gradient = (20 − 0) ÷ 4 = 5 m s⁻².
Distance = area = ½ × 4 × 20 (triangle) + 20 × 6 (rectangle) = 40 + 120 = 160 m.
Reading shapes
A straight sloping line on a v–t graph means uniform acceleration; a curve means changing acceleration.
Remember
- s–t gradient = velocity.
- v–t gradient = acceleration; v–t area = distance.
- Break the area into triangles and rectangles.