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A.1.3—Displacement

Syllabus
First assessment 2025
Objective
—
Level
HL

Define Displacement as Change in Position

Displacement is a vector

Displacement is the change in position:

Δr⃗=r⃗final−r⃗initial\Delta\vec r=\vec r_{final}-\vec r_{initial}

It has a magnitude and a direction from the initial position to the final position.

Ignore the route for displacement

The path taken between the two positions does not determine displacement. A curved or complicated journey can still have a straight-line displacement between its endpoints.

Use components when needed

For perpendicular changes, resolve displacement into components and combine them vectorially. A signed one-dimensional displacement is positive or negative according to the chosen axis.

Common trap

A return to the starting point gives zero displacement even though the distance travelled is non-zero.

A.1.3 Exam Analysis

[ 1 ]

A stone is kicked horizontally at a speed of 1.5 ms−11.5 \mathrm{~ms}^{-1} from the edge of a cliff on one of Jupiter's moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m .
Air resistance is negligible.
What is the magnitude of the displacement of the stone?

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.