Area under a velocity-time graph gives distance travelled
3 marks · NormalA runner moves at first with increasing speed, then at a steady speed, and finally slows to a stop. Describe how her velocity–time graph would look, and explain how you would calculate the total distance travelled from the graph.
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The graph would start with a section that slopes upward (increasing velocity), followed by a horizontal line (constant velocity), and end with a section that slopes downward to zero (decreasing velocity). To find the total distance, you divide the area under the graph into shapes (triangles and rectangles), calculate each area, and add them together. The total area under the curve gives the total distance.
Must show: Describes graph: increasing, constant, decreasing sections, States to divide area under graph into shapes, Explains sum of all areas equals distance
Common mistakes: Describing position-time graph; Not mentioning the need to add all relevant areas
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Marking points
B1 · 1 mark · Correct description: upward slope, flat, downward slope in graph.
B2 · 1 mark · States that areas under each section (geometry or by calculating strips) give part of total distance.
B3 · 1 mark · Explains that total distance is the total area under the velocity–time graph.
Worked solution
The velocity–time graph would start with a sloped line upwards, showing increasing speed (acceleration); then a flat horizontal section, showing constant speed; and then a sloped line down to zero, showing deceleration as she stops. To calculate the total distance, find the area under each section of the graph (the two triangles and the rectangle), then add all areas to get the total distance.