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
[ 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
Magnitude of average
velocity /ms−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.