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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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  3. Histograms Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  35. Functions Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  55. Introduction Aqa Higher
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Exam code:8300

Speed-time graphs

How do I use a speed-time graph?

  • Kinematics is the study of motion of objects

    • It looks at how an object moves over time

  • Speed-time graphs show the speed of an object at different times

    • Speed is on the vertical axis

    • Time is on the horizontal axis 

  • The gradient of the graph is the acceleration

    • Acceleration space equals space speed over time space equals space rise over run

  • A positive gradient shows positive acceleration (speeding up)

  • A negative gradient shows negative acceleration, (slowing down)

    • This is also called deceleration

Acceleration examples - a car decelerating as it brakes, and a rocket accelerating up towards space

  • Horizontal lines indicate moving at a constant speed

    • The object is neither speeding up or slowing down

    • If the constant speed is zero, then it is at rest

  • A straight line shows constant acceleration

  • A curve shows changing acceleration

    • To find the acceleration at a particular point on the graph

      • draw a tangent to the graph at this point and find its gradient

A graph showing tangents drawn at two points, A and B, on a curve. The tangent at point A has a shallow gradient and the tangent at point B has a steeper gradient.

  • The distance covered by the object is the area under the graph

    • Split the area into simple shapes, e.g. rectangles and triangles

    • Find the area of each shape and add them together

Examiner Tips and Tricks

  • Always check the vertical axis to see if you are given a speed-time graph or a distance-time graph!

Worked Example

The speed-time graph for a car travelling between two sets of traffic lights is shown below. 

real-life-graphs-s-t-graph-we-image

(a) For how long was the car travelling at a constant speed?

Constant speed is represented by horizontal lines

There is a horizontal line from 6 seconds to 15 seconds

15 – 6 = 9

9 seconds

(b) Calculate the acceleration during the first 6 seconds. 

In a speed-time graph the acceleration is the gradient of the graph

acceleration space equals space fraction numerator space rise over denominator run end fraction equals space speed over time

<img alt=”real-life-graphs-s-t-graph-we-image-2″ class=”ContentBlock_figure__vJw2q” data-nimg=”1″ decoding=”async” height=”1787″ loading=”lazy” sizes=”(max-width: 320px) 320w, (max-width: 640px) 640w, (max-width: 960px) 960w

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