Describing Motion Around Us
Velocity-time graphs
Read velocity-time graphs to find acceleration and displacement.
A different graph. Now time goes along the bottom and velocity goes up the side. Each point says: 'at this time, it was going this fast'. Its shape tells the story.
Three shapes to know.
- Flat line: the velocity is not changing, so the acceleration is zero. A car at a steady 72 km h⁻¹ (= 20 m s⁻¹) draws a flat line at 20.
- Straight line going up: the velocity rises by equal amounts in equal times (Table 4.5: 0, 2.5, 5.0 … 15.0 m s⁻¹, every 5 s). That is constant acceleration.
- Straight line going down: the velocity falls steadily (Table 4.6: 15.0 down to 0). The object is slowing down at a constant rate.
The slope is the acceleration. Slope = how much the velocity rose ÷ how much time passed. That is exactly the meaning of acceleration. From (10 s, 5 m s⁻¹) to (20 s, 10 m s⁻¹): a = 5 ÷ 10 = 0.5 m s⁻². For the falling line in Table 4.6 it is –0.5 m s⁻².
The area under the line is the displacement. Why? Distance = velocity × time. On this graph, velocity is the height and time is the width. Height × width is an area. So the area under the line tells you how far the object went.
A rectangle. A steady 20 m s⁻¹ for 6 s: the shape under the line is a rectangle, 20 high and 6 wide. Area = 20 × 6 = 120 m.
A rectangle plus a triangle. The velocity rises from 5 to 10 m s⁻¹ between 10 s and 20 s. Cut the shape under the line into two pieces:
- the rectangle underneath: 5 × 10 = 50 m;
- the triangle on top: ½ × 10 × 5 = 25 m.
Displacement = 50 + 25 = 75 m.
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