AI generatedRatio, proportion and rates of changeKS3 / GCSE

Drawing a velocity-time graph

Drawing a velocity-time graph.

  • A velocity–time graph shows velocity vertically and time horizontally.
  • Its gradient gives acceleration; its signed area gives displacement.
  • For distance, add the magnitudes of areas if the graph goes below the time axis.

Example 1

A cyclist accelerates uniformly from rest to 12 in 2 s, keeps that velocity for 2 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph12345678510150ABC

Example 2

A cyclist accelerates uniformly from rest to 13 in 3 s, keeps that velocity for 2 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph123456789510150ABC

Your turn

Question 1

A cyclist accelerates uniformly from rest to 14 in 4 s, keeps that velocity for 2 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Check answer
Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph12345678910510150ABC
Question 2

A cyclist accelerates uniformly from rest to 15 in 5 s, keeps that velocity for 2 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Check answer
Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph1234567891011510150ABC
Question 3

A cyclist accelerates uniformly from rest to 16 in 6 s, keeps that velocity for 2 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Check answer
Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph12345678910111251015200ABC
Question 4

A cyclist accelerates uniformly from rest to 17 in 2 s, keeps that velocity for 3 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Check answer
Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph12345678951015200ABC
Question 5

A cyclist accelerates uniformly from rest to 18 in 3 s, keeps that velocity for 3 s, then slows uniformly to rest over 3 s. Draw a velocity–time graph.

Check answer
Key timesUse cumulative time, not the duration of each part.
HeightsJoin the matching points with straight segments.
Label both axes and units. Each straight segment represents a constant rate of change.
Coordinate graph1234567891051015200ABC
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