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A.1.4—Distance and displacement

Syllabus
First assessment 2025
Objective
—
Level
SL

Distinguish Distance and Displacement

Distance

Distance is the total path length travelled. It is a scalar, so it has magnitude only and cannot be negative.

Displacement

Displacement is the vector change in position from start to finish. Its magnitude is the shortest endpoint-to-endpoint separation, not generally the length of the route.

Match the average quantity

Average speed uses total distance divided by total time. Average velocity uses displacement divided by total time. A route with turns can therefore have average speed greater than the magnitude of average velocity.

Common trap

For a complete oscillation, the displacement is zero but the distance is four times the amplitude. Choose the quantity named in the question before substituting.

A.1.4 Exam Analysis

Assessment in practice

1–3 marks
How it is assessed

The evidence compares average speed and average velocity for a person taking two legs and asks for distance travelled during one complete oscillation.

Command terms

Calculate / Distinguish

What earns marks

Use total path length for average speed and endpoint displacement for average velocity. In a complete oscillation, calculate distance from the repeated path segments; for a route with perpendicular legs, use the resultant displacement and total distance separately.

Watch for

Using displacement in the average-speed calculation or using total distance in the average-velocity calculation.

Representative question

Question 1

[Maximum number: 1]

A person walks 40 m due west and then 30 m due north. The total walking time is 100 s . What are the average speed and the magnitude of the average velocity of the person?

Average speed/m s −1{ }^{-1}

Magnitude of average
velocity /ms−1/ \mathrm{m} \mathrm{s}^{-1}

0.5

0.5

0.5

0.7

0.7

0.5

0.7

0.7

Retrieve the A.1 Kinematics Model

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.