GCSE Physics (AQA)

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Area Under a Velocity-Time Graph

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Forces Forces and motion

Area Under a Velocity-Time Graph

6:09 Velocity-Time Graphs
Spec 4.5.6.1.5
Previous Newton's Second Law Next Acceleration Due to Gravity
  • The area under a velocity-time graph represents the distance traveled during that time.
  • A velocity-time graph shows an object's velocity at each point in time, with the gradient indicating acceleration.
  • A horizontal graph with no gradient indicates constant velocity and no acceleration.
  • The relation between speed and distance is given by the equation: Speed = Distance / Time (V = S / T).
  • Rearranging the equation gives VT = S, where V is velocity, T is time, and S is distance.
  • For a constant velocity, the area under the graph (a rectangle) is calculated as base (T) times height (V), equating to distance (S).
  • For changing velocity, the area under the graph is found by dividing the shape into triangles and rectangles.
  • The area of a triangle is calculated using 0.5 * base * height, and for a rectangle, it's base * height.
  • In exams, you may need to calculate the area under a velocity-time graph to find the distance traveled.
  • Example problem: Calculate the distance a dog runs using a velocity-time graph by splitting the graph into shapes and calculating each area.
  • Steps include splitting the graph into triangles and rectangles, calculating each area, and summing them to find the total distance.
  • Example calculation: Total distance = 7 meters (first triangle) + 10.5 meters (rectangle) + 12.25 meters (last triangle) = 29.75 meters.

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