A graph is not a map

The idea

A motion graph shows how position, velocity or acceleration changes with time; it is not a route map and does not show the path taken, only how position changes with respect to the origin.

Numbers into a picture

A table lists the position of a vehicle at 0 s, 1 s, 2 s and so on. A friend says, "Let us draw a graph of it."

What do you think the graph will show?

• How the position changes with time
• The exact road the vehicle took
• The colour of the vehicle

From table to graph

Press Next step to go from the road to the graph.

What a graph tells

The table became a line on a graph. The line slopes upward because the position grows as time passes. It does not tell us whether the road was flat, hilly or bending. A motion graph shows how a quantity such as position changes with time.

A motion graph shows how position, velocity or acceleration changes with time. A graph is not a route map: it does not show the path taken, only how the position changes with respect to the origin.

Notes

A motion graph shows how position, velocity or acceleration changes with time. It is not a route map.

Check yourself

What does a position-time graph of a vehicle show?

A vehicle moves along a flat straight road and its position-time graph slopes upward. What does the upward slope tell us?

Use Table 4.3: what is the position of the vehicle at 5 s?

Answer: 100 m

At 5 s the vehicle is 100 m from the origin.

Which of these can a motion graph show changing with time?

• The path the vehicle took, like a map. A graph is not a route map. It does not show the path, only how the position changes with time.
• How the position of the vehicle changes with time — correct. Yes!
• The shape of the road. The road is not drawn on the graph. Only the change of position with time is.
• The road climbs a hill. A graph is not a route map. The slope shows how position changes with time, not the shape of the road.
• The vehicle is at rest. A vehicle at rest does not change its position, so its graph would not slope upward.
• Only that its position increases with time, not anything about the road — correct. Yes!
• Velocity — correct. Yes!
• The shape of the road. A graph is not a route map, so it does not show the road.
• The colour of the vehicle. Colour does not change the motion. A motion graph shows position, velocity or acceleration against time.