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GB-29-05-001 · Velocity–time graph area

17133842Time (s)Velocity (m/s)
Diagram not accurately drawn

A vehicle accelerates uniformly from rest to 17 m/s in 13 s. It maintains this velocity for 25 s, then slows uniformly to rest in 4 s. Find the total distance travelled.

Velocity–Time Graphs: Distance Travelled Booklet p. 58
Method
1) Area under a velocity–time graph represents DISTANCE TRAVELLED
2) Split into triangles/rectangle (or trapezium) and add areas
Worked Example (GB-29-05-001)
Booklet p. 58: Area under V–T graph = Distance (Area 1◯+Area 2◯+Area 3◯\text{Area }\textcircled{1} + \text{Area }\textcircled{2} + \text{Area }\textcircled{3}) · Gradient = Acceleration (y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1})
1) Find the area under the velocity–time graph.
2) ½ × 13 × 17 + 25 × 17 + ½ × 4 × 17.
3) 569.5 m
569.5 m