Distance–time and velocity–time graphs
Distance–time graphs
A distance–time graph plots distance travelled (y-axis) against time (x-axis).
- Gradient = speed. The steeper the line, the faster the object.
- Horizontal line → object is stationary.
- Straight diagonal line → constant speed.
- Curve → changing speed (acceleration or deceleration).
Speed is calculated as: speed = change in distance ÷ change in time.
For a curve, you find the speed at a particular instant by drawing a tangent at that point and calculating its gradient.
Velocity–time graphs
A velocity–time graph plots velocity (y-axis) against time (x-axis). Velocity has direction; speed does not.
- Gradient = acceleration (a = Δv ÷ Δt, units m/s²).
- Horizontal line → constant velocity (zero acceleration).
- Straight diagonal line going up → constant acceleration.
- Straight diagonal line going down → constant deceleration.
- Line below the time axis → motion in the opposite direction.
Area under a velocity–time graph
The area between the line and the time axis = distance travelled. This is hugely useful in exam questions.
- For a rectangle (constant velocity): area = velocity × time.
- For a triangle (uniform acceleration from rest): area = ½ × base × height.
- For a trapezium: area = ½ × (a + b) × h, where a and b are the two parallel sides.
For curved v–t graphs, count squares on the gridded paper or split into rectangles/triangles to estimate.
✦Worked example
A car accelerates uniformly from 0 to 20 m/s in 8 s, then drives at 20 m/s for 12 s.
- Acceleration = (20 − 0) ÷ 8 = 2.5 m/s².
- Distance during acceleration = ½ × 8 × 20 = 80 m.
- Distance at constant velocity = 20 × 12 = 240 m.
- Total distance = 320 m.
Edexcel exam tip
Always state units (m/s for speed, m/s² for acceleration, m for distance). When asked to "describe the motion", quote three things: the direction (forwards/backwards), whether it is speeding up / slowing down / constant, and any pauses.
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