Example 1 · level 1
A car starts from rest and its velocity increases uniformly to 20 m/s in 4 s (see the v–t graph). Find the distance covered (in m).
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- Area of triangle = ½ × 4 × 20 = 40 m.
Answer: 40 m
CLASS 9 SCIENCE · MOTION
Distance from a velocity–time graph
The area under a velocity–time graph equals the distance travelled (for motion in one direction). Split it into rectangles and triangles.
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Worked examples
Example 2 · level 2
A metro train starts from rest, reaches 16 m/s uniformly in 4 s and then runs at that steady speed until t = 9 s. Find the total distance covered (in m).
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- Triangle: ½ × 4 × 16 = 32 m.
- Rectangle: 5 × 16 = 80 m.
- Total = 112 m.
Answer: 112 m
Example 3 · level 3
A bus starts from rest, speeds up uniformly to 16 m/s in 6 s, moves steadily till t = 10 s, then slows uniformly to stop at t = 16 s. Find the total distance (in m).
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- Speeding up: 48 m.
- Steady: 64 m.
- Slowing down: 48 m.
- Total = 160 m.
Answer: 160 m