Distance-Time Graphs (Edexcel IGCSE Maths)

Spec point — 3.3F

Distance-time graphs

How do I use a distance-time graph?

• Distance-time graphs show the distance travelled at different times

  • Distance is on the vertical axis
  • Time is on the horizontal axis

• The gradient of the graph is the speed

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

• The steeper the line the faster the object is moving

  • Lines with positive gradients represent objects moving away from the start point

  • Lines with negative gradients represent objects moving towards the start point

  • Lines that are horizontal represent rest

    • The object is stationary (not moving)

How do I work out the overall average speed?

• For journeys with multiple parts

  • the overall average speed for the whole journey is $\frac{\mathrm{total} \mathrm{distance} \mathrm{travelled}}{\mathrm{total} \mathrm{time}}$
  • The total time includes any rests

Exam Hint These questions often have a lot of parts that depend on each other, so always double check each answer before continuing.

Worked Example One afternoon, Mary jogged 8 km from her home to her grandfather's house. Part of the travel graph for her journey is shown.

(a) Find Mary's speed at 2 pm.

Answer:

The speed is the gradient of the line at that point The gradient at 2pm is the same as the gradient for all points between 1:45pm and 2:45pm It is easiest to use $\frac{\mathrm{rise}}{\mathrm{run}}$ for that bigger section

$\frac{\mathrm{rise}}{\mathrm{run}}=\frac{6}{1}$

Final answer: 6 km/h

(b) Calculate, in minutes, how long Mary stopped on the way to her grandfather's house.

Answer:

The horizontal line is where Mary stops The scale is 1 square = 15 minutes

Final answer: 15 minutes

(c) Calculate Mary's overall average speed from leaving her home to arriving at her grandfather's house, giving your answer correct to 3 significant figures.

Answer:

Overall average speed is $\frac{\mathrm{total} \mathrm{distance} \mathrm{travelled}}{\mathrm{total} \mathrm{time}}$* *

Total distance travelled is 8 km Total time (including rests) is 1.75 hours

$\frac{8}{1.75}=4.57142...$

Round the answer to 3 significant figures

Final answer: 4.57 km/h (to 3 s.f.)

(d) Mary stayed at her grandfather's house for half an hour, then jogged home at a steady speed without stopping, arriving home at 4pm.

Complete the travel graph for Mary's journey.

Answer:

Rest is a horizontal line Returning home is a straight line with a negative gradient