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Instantaneous Speed — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions

5 min read 7 parts Lesson 26 of 44

📚 AQA GCSE Combined Science Trilogy 8464 - Physics Hub / Topical Revision
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Part 1 of 5Curves on distance–time graphs

Graph shapeMeaningSpeed
Straight, sloping lineConstant speedGradient is the same everywhere
Curve getting steeperAcceleratingSpeed increases
Curve getting flatterDeceleratingSpeed decreases
Horizontal lineStationaryZero

Part 2 of 5Why a tangent is needed

Gradient equals speed
  • Gradient equals speed On a distance–time graph, the gradient of the line is the speed.
Gradient changes on a curve
  • Gradient changes on a curve The steepness is different at each point, so no single gradient describes the whole curve.
Instantaneous speed
  • Instantaneous speed The speed at one particular moment is the gradient of the curve at that point, found using a tangent.

Part 3 of 5Finding speed at a time

1
Locate the time on the horizontal axis and go up to the point on the curve.
2
Place a ruler so that it just touches the curve at that point.
3
Adjust it until the angle between ruler and curve looks the same on both sides of the point, then draw the tangent line.
4
Make the tangent long, then choose two points far apart on it and read their time and distance values.
5
Calculate gradient = change in distance ÷ change in time. The answer is the speed in m/s.

Part 4 of 5Improving accuracy

Drawing a good tangent
Touch only once
  • Touch only once The line should touch the curve only at the chosen point, not cut across it.
Use a long triangle
  • Use a long triangle A large right-angled triangle on the tangent reduces the error in reading the values.
Read with care
  • Read with care Use the axis scales and units, and work out each interval from the graph, not from the plotted points.

Part 5 of 5Linking motion to graph

1Object accelerates
  • Object accelerates Distance increases by larger amounts each second.
2Curve steepens
  • Curve steepens The line bends upwards on the graph.
3Tangent steeper
  • Tangent steeper Later tangents have larger gradients.
4Speed higher
  • Speed higher The instantaneous speed is greater at later times.

Key terms

TermMeaning
Instantaneous speedThe speed of an object at one particular moment in time.
TangentA straight line that touches a curve at one point and has the same gradient as the curve there.
GradientThe change in the vertical value divided by the change in the horizontal value.
Distance–time graphA graph showing how far an object has travelled as time passes.
DecelerationA decrease in speed.

Avoid these mistakes

1
Drawing the tangent so that it crosses the curve instead of just touching it.
2
Using two points on the curve instead of two points on the tangent to find the gradient.
3
Using a very short tangent, which makes the gradient inaccurate.
4
Reading the height of the curve as the speed; the speed is the gradient, not the distance value.

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