Theme A — Space, Time and Motion
Theme A — Space, Time and Motion — IB Physics SL Revision Notes & Topical Questions
5 min read 11 parts Lesson 1 of 41 Unit quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
Theme A — Space, Time and Motion — IB PHYSICS SL notes: Summarise motion, forces, momentum, circular motion, work, energy and power at IB Physics SL level.Distance — total path length; a scalar.Displacement — change in position in a stated direction; a vector.Velocity — the rate …
- Acceleration
- Projectile
- Terminal speed
- Resultant force
- Second law
- Conservation of linear momentum
Section 1 of 11Kinematics: distance, displacement, speed and velocity
Distance
- Distance total path length; a scalar.
Displacement
- Displacement change in position in a stated direction; a vector.
Velocity
- Velocity the rate of change of displacement; speed is distance per unit time and is a scalar.
Acceleration
- Acceleration the rate of change of velocity, a vector in m s−2.
- A negative value means acceleration in the negative direction, not necessarily slowing down.
Average velocity = total displacement ÷ total time; instantaneous velocity is the gradient of a tangent to the displacement-time graph.
Free fall is motion under gravity alone with acceleration g.
Section 2 of 11Equations and graphs of motion
What the symbols mean:
For uniform acceleration:
- v = u + atWhat the symbols mean: v = final velocity (m s−1) · u = initial velocity (m s−1) · a = acceleration (m s−2) · t = time (s)
- s = ut + ½at2What the symbols mean: s = displacement (m) · u = initial velocity (m s−1) · a = acceleration (m s−2) · t = time (s)
- v2 = u2 + 2asWhat the symbols mean: v = final velocity · u = initial velocity (m s−1) · a = acceleration (m s−2) · s = displacement (m)
- s = ½(u + v)tWhat the symbols mean: s = displacement (m) · u = initial velocity · v = final velocity (m s−1) · t = time (s); (u + v)/2 is the average velocity
Choose a positive direction and keep to it for every vector.
On a displacement-time graph the gradient is velocity.
On a velocity-time graph the gradient is acceleration and the area is displacement.
On an acceleration-time graph the area is the change in velocity.
Section 3 of 11Projectiles and fluid resistance
Projectile
- Projectile moves freely under gravity in two dimensions.
- Horizontal and vertical motion are independent.
- Horizontal velocity is constant;
- vertical acceleration is g;
- resolve the launch velocity into u cos θ and u sin θ.
Fluid resistance (viscous drag) opposes motion and increases with speed.
- It lowers the range and maximum height, shortens the flight time and makes the path steeper on the way down.
Terminal speed
- Terminal speed reached when the drag force equals the weight, so acceleration is zero.
Section 4 of 11Forces and Newton's laws
1
A free-body diagram shows all forces on one object as arrows from a point mass.
- Common forcesweight (towards the planet), tension, normal reaction (perpendicular to a surface) and friction.
2Resultant force
- Resultant force the vector sum of the forces.
3First law
- First law a body stays at rest or at constant velocity unless acted on by a resultant force;
- zero resultant means translational equilibrium.
4Second law
- Second law resultant force = rate of change of momentum, and F = ma for constant mass.
5Third law
- Third law the forces of two interacting objects are equal, opposite, of the same type and act on different objects.
Section 5 of 11Types of force
| Force | Key points |
|---|---|
| Contact forces | Friction, drag, tension and normal force act between touching objects |
| Non-contact forces | Gravitational, electrostatic and magnetic forces act at a distance through fields; weight = mg |
| Friction | Opposes relative motion; static friction ≤ μsFN, dynamic friction = μdFN; it transfers energy as heat |
| Hooke's law | F = kx up to the limit of proportionality; k is the gradient of the force-extension graph |
| Stokes' law | Fd = 6πηrv for a sphere in a fluid |
| Buoyancy | Fb = ρVg, with ρ the fluid density and V the volume displaced |
Section 6 of 11Momentum and impulse
Momentum and impulse
Momentum p = mv; it is a vector in kg m s−1.
Conservation of linear momentum
- Conservation of linear momentum total momentum before equals total momentum after unless an external resultant force acts.
What the symbols mean:
Impulse J = FΔt = Δp = mv − mu.
What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
- A longer contact time lowers the force for the same change of momentum.
Collisions: momentum is always conserved.
- Elastic — kinetic energy conserved.
- Inelastic — kinetic energy not conserved.
- Totally inelastic — objects stick together and the maximum kinetic energy is dissipated.
In an explosion the objects start at rest and kinetic energy is not conserved.
Section 7 of 11Circular motion
1
Angular displacement θ = s ÷ r in radians; one revolution is 2π rad.
2
Angular speed ω = Δθ ÷ Δt = 2π ÷ T = 2πf, and linear speed v = ωr.
3
In uniform circular motion speed is constant but velocity changes, so there is acceleration towards the centre.
- Centripetal acceleration a = v2 ÷ r = ω2r.
- Centripetal force F = mv2 ÷ r = mω2r, perpendicular to the velocity, so it does no work.
4
The centripetal force is not a separate force: it is provided by tension, friction, gravity or the normal force.
5
In vertical circles the tension is greatest at the bottom and least at the top.
Section 8 of 11Work, energy and power
1
Work done = transfer of energy; W = Fs cos θ with θ the angle between force and displacement.
2
The area under a force-displacement graph equals the work done.
3
Kinetic energy Ek = ½mv2 = p2 ÷ 2m.
4
Gravitational potential energy change ΔEp = mgΔh in a uniform field.
5
Elastic potential energy EH = ½kx2 = ½Fx.
6
Mechanical energy = Ek + Ep + EH and is conserved only when no resistive forces act.
7
Power P = W ÷ t = Fv; 1 W = 1 J s−1.
Section 9 of 11Energy transfers and efficiency
Energy cannot be created or destroyed, only transferred.
No transfer is 100% efficient; dissipated energy is usually thermal and counted as wasted.
Sankey diagram
- Sankey diagram arrow width is proportional to energy; total in = useful out + wasted.
Efficiency η = useful output ÷ total input (energy or power), as a ratio or percentage, with no units.
Energy density
- Energy density energy per unit volume of fuel, in J m−3.
Section 10 of 11Key terms
| Term | Meaning |
|---|---|
| Displacement | Change in position in a stated direction. |
| Acceleration | Rate of change of velocity. |
| Terminal speed | Constant speed when drag equals weight. |
| Impulse | Force multiplied by the time it acts; equals change in momentum. |
| Centripetal force | Resultant force towards the centre of a circular path. |
| Hooke's law | Extension is proportional to force up to the limit of proportionality. |
| Work done | Energy transferred by a force moving an object. |
| Efficiency | Useful output divided by total input. |
Section 11 of 11Exam technique
1
Squaring only part of the kinetic energy expression or forgetting to square the speed.
2
Adding a separate centripetal force to a free-body diagram — it is the resultant of the real forces.
3
Treating two equal and opposite forces on one object (weight and normal force) as a Newton's third-law pair.
4
Assuming kinetic energy is conserved in every collision — only in elastic ones.
5
Using km h−1 without converting to m s−1, or degrees instead of radians for ω.
Last updated:
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).