Distance-Time & Speed-Time Graphs (OCR GCSE Maths)

How does a distance-time graph work?

• Distance-time graphs show distance from a fixed point at different times
  • Distance is on the vertical axis, and time is on the horizontal axis.
•  The gradient of the graph is the speed
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• A positive gradient represents the object (or person) moving away from the starting point
• If the graph is a horizontal line the object is stationary (not moving)
• A negative gradient represents the object (or person) moving towards the starting point
• If the graph is a straight line the speed is constant
• If the graph is a curve you can find an estimate of the speed at a point by drawing the tangent at a point on the graph and find its gradient
• To find the average speed through a period of time, divide the total distance in that time period by the total time
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What is a speed-time graph?

• Speed-time graphs show speed at different times
  • Speed is on the vertical axis, and time is on the horizontal axis
• The gradient of the graph is the acceleration

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• If the graph is a curve you can
  • estimate of the acceleration at a point by drawing the tangent at that point on the graph and finding its gradient
  • find the average acceleration between two points by drawing a chord between the two points and finding its gradient
• A positive gradient shows positive acceleration (speeding up)
• A horizontal line on a speed-time graph shows constant speed (no acceleration)
• A negative gradient shows negative acceleration, or deceleration (slowing down)

• The distance covered can be found by finding the area under the graph
• If the graph is a curve you can estimate the distance covered by drawing trapeziums underneath the graph and finding their area