Kinematics
Displacement, Velocity & Acceleration · SUVAT Equations & Projectile Motion · Relative Motion & Frames of Reference
IB Physics SL topic guide
Space, Time and Motion
Space, Time and Motion is a core part of IB Physics SL. This guide connects the syllabus ideas behind Kinematics, Forces and Momentum, Work, Energy and Power, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.
What you will learn
Space, Time and Motion syllabus outline
The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.
Forces and Momentum
Newton's Laws of Motion · Momentum & Impulse · Friction, Drag and Terminal Velocity
Work, Energy and Power
Work and Energy · Power and Efficiency · Energy Sources and Transformations
Free worked preview
Displacement, Velocity & Acceleration
This complete preview comes from the Kinematics unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.
Displacement, Velocity & Acceleration
Kinematics supplies the mathematical language for describing every kind of motion — from the free-fall of an apple to the orbital velocity of a satellite. Every later topic, from SUVAT to projectile paths to centripetal acceleration, builds directly on the definitions below. It describes motion without reference to its cause, and it starts by distinguishing scalar quantities (magnitude only) from vector quantities (magnitude and direction).
| Scalar | Vector Equivalent | SI Unit |
|---|---|---|
| Distance d | Displacement s | m |
| Speed v | Velocity v | m s⁻¹ |
| — | Acceleration a | m s⁻² |
Core Definitions
Average velocity is the total displacement divided by the total time taken. In symbols, with Δ meaning "change in":
Instantaneous velocity is the velocity at one specific instant — found by making Δt infinitesimally small. In calculus notation:
Acceleration is the rate of change of velocity:
Average velocity is the total displacement divided by the total time taken. In symbols, with Δ meaning "change in":
where
change in displacement = final position − initial position (m)
time interval (s)
average velocity (m s^{-1})
Acceleration is the rate of change of velocity:
where
change in velocity = final velocity − initial velocity (m s⁻¹)
time interval (s)
acceleration (m s^{-2}) — negative value means the object is slowing down (if moving in +ve direction)
Motion Graphs
- Displacement–time (s–t): gradient = instantaneous velocity; curved line = non-uniform velocity
- Velocity–time (v–t): gradient = acceleration; area under graph = displacement (signed)
- Acceleration–time (a–t): area under graph = change in velocity
Worked Example
A car accelerates uniformly from rest to 24 m s⁻¹ in 6 s, then travels at constant speed for 10 s.
Displacement (acceleration phase) = area of triangle = ½ × 6 × 24 = 72 m
Displacement (constant phase) = 24 × 10 = 240 m
Total displacement = 312 m
Displacement (acceleration phase) = area of triangle = ½ × 6 × 24 = 72 m
Displacement (constant phase) = 24 × 10 = 240 m
Total displacement = 312 m
Common ErrorA negative gradient on a v–t graph means deceleration — but the object is still moving forward if v is positive. The object reverses direction only when v crosses zero.
Reviewed by the Study to Learn editorial team · Updated 2026-07-24