Speed-Time Graphs (Edexcel IGCSE Maths)

Spec point — 4.4F

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

  • $\mathrm{Acceleration}=\frac{\mathrm{speed}}{\mathrm{time}}=\frac{\mathrm{rise}}{\mathrm{run}}$

• A positive gradient shows positive acceleration (speeding up)

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

  • This is also called deceleration

• 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

• 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

Exam Hint 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.

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

Answer:

Constant speed is represented by horizontal lines

There is a horizontal line from 6 seconds to 15 seconds

15 - 6 = 9

Final answer: 9 seconds

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

Answer:

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

$\mathrm{acceleration}=\frac{\mathrm{rise}}{\mathrm{run}}=\frac{\mathrm{speed}}{\mathrm{time}}$

$\mathrm{acceleration}=\frac{9m/s}{6s}=1.5\frac{m/s}{s}$

Final answer: Acceleration = 1.5 m/s²

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

Answer:

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 *$\text{Area} = \frac{( a + b ) h}{2}$

• *$\text{Area} = \frac{( 9 + 20 ) \times 9}{2} = \frac{261}{2} = 130.5$

Final answer: Distance travelled = 130.5 m