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iGCSE (2021 Edition)

15.05 Travel graphs

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Travel graphs are a way to describe the movement of people or objects. They usually describe a trip that leaves and returns to a point (like a home base).

The vertical axis of a travel graph is the distance travelled from a starting point and the horizontal axis is the time taken from the starting point.

 

Reading a travel graph

There are certain important features of a travel graph that we can use to interpret the journey being described:

  • As the line moves away from the horizontal axis, the object is moving further away from the "home" point
  • As the line moves back towards the horizontal axis, the object is returning home
  • When the line is horizontal, the object is not moving
  • The steeper the line, the greater the speed of the an object (the faster it moves)
  • A straight line indicates a steady speed
  • The total distance of the trip is the distance away from and returning home

 

Worked example

Consider the following graph which displays a day long car tip with the horizontal axis being time in hours and the vertical axis being distance from home in kilometres:

(a) What speed did the car travel in the first hour? (Extended)

Think: We know that $$Speed=DistanceTime​. How far did they travel in the first hour?

Do:

Speed $$= $$DistanceTime​
  $$= $$80 km1 h​
  $$= $$80 km/h

(b) What happened between the times of $$1 and $$2?

Think: What does it mean for the graph to be horizontal?

Do: The car was stationary for $$1 hour. Perhaps a break for lunch or a visit to a park.

 

(c) How far is the car from home after $$6 hours?

Think: Read the vertical axis for the distance at $$6 hours.

Do: The car is $$50 km from home.

 

(d) What was the average speed of the car over the $$6 hour journey? (Extended)

Think: How far has the car travelled in total? The car initially travelled $$80 km, then was stationary for one hour, then travelled a further $$120 km before starting the return tip home at $$4 hours into the journey. In the last section of the journey they are returning to home from $$200 kilometres away and reach $$50 kilometres from home, thus they travel $$150 km.

Do:

Total distance travelled $$= $$80+120+150 km
  $$= $$350 km

 

Average speed $$= $$Total distancetime​
  $$= $$350 km6 h​
  $$= $$58.3 km/h

 

Practice questions

Question 1

Which graph shows the height of a ball being thrown vertically into the air?

  1. A

    B

    C

    D

Question 2

Ben travels forwards and backwards along a straight line.

The graph shows Ben's distance from his starting point at various times of the day.

A line graph is displayed with the horizontal axis labeled "Time" marked from 9 to 5 in one-hour increments, and the vertical axis labeled "Distance (km)" marked from 0 to 300 in increments of 50. A line connects several points on the graph, starting at <mi>coord(9, 0)</mi>, to <mi>coord(11, 150)</mi>, to <mi>coord(1, 250)</mi>, to <mi>coord(2, 250)</mi>, to <mi>coord(3, 100)</mi>, and ending at <mi>coord(4, 0)</mi>.

  1. When did Ben start his journey?

  2. How far did Ben travel by $$11 am?

  3. What happened to Ben's speed at $$11 am?

    Ben decreased his speed at $$11 am.

    A

    Ben did not change his speed at $$11 am.

    B

    Ben increased his speed at $$11 am.

    C

  4. Evaluate Ben's speed between $$11 am and $$1 pm.

  5. What distance did Ben travel between $$1 pm and $$2 pm?

  6. What is the furthest distance travelled from the starting point?

  7. What is the total distance travelled by Ben from $$9 am to $$4 pm?

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