Displacement includes both the distance an object moves, measured in a…

The idea

Displacement is measured in a straight line from where the object started to where it finished, and it carries a direction as well as a length. On a scale map of a winding railway, the distance travelled is the length of the track while the displacement is the straight arrow drawn from the first station to the second, measured with a ruler and converted using the scale. Walk three metres east and then four metres north and the distance is seven metres, but the displacement is five metres on a bearing of 037 degrees, because the two legs combine as a right-angled triangle. Any journey that returns to its starting point has zero displacement however far it travelled, and displacement can never exceed distance.

What earns the marks

• The straight line measured from the start point to the finish point.
• A direction stated as well as a magnitude.
• Measuring a displacement from a scale drawing and applying the scale.
• Recognising that the displacement is zero for a journey that returns to its start.

Common mistakes and how to put them right

• Quoting a displacement with no direction attached.

• Adding the legs of a journey arithmetically instead of combining them as a triangle.

• Using the path length as the displacement on a curved route.

• Forgetting to apply the scale when measuring from a drawing.

Exam tips

• Measure with a ruler and show the scale conversion; both steps are credited.
• If the start and the finish coincide, write zero straight away without calculating.