Speed-Time Graphs (Edexcel IGCSE Maths A (Modular))

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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)

  • 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

real-life-graphs-s-t-graph-we-image-2

acceleration space equals space fraction numerator 9 space straight m divided by straight s over denominator 6 space straight s end fraction space equals space 1.5 space fraction numerator straight m divided by straight s over denominator straight s end fraction

Acceleration = 1.5 m/s2

(c) Work out the distance covered by the car. 

In a speed-time graph the distance travelled is equal to the area under the graph

 The graph is a trapezium so use the formula   Area space equals space fraction numerator open parentheses a space plus space b close parentheses h over denominator 2 end fraction

  Area space equals space fraction numerator open parentheses 9 space plus thin space 20 close parentheses space cross times space 9 over denominator 2 end fraction space equals space 261 over 2 space equals space 130.5 space

  Distance travelled = 130.5 m

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Amber

Author: Amber

Expertise: Maths

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.