A-Level Physics: Motion & Forces Guide

TL;DR
Graphs, Kinematics and Dynamics sit at the heart of every Motion & Forces question.
Nail the language (position vs displacement), pick the right graph tool (area or gradient) and keep a one-page suvat cheat-sheet handy. This post turns the SEAB bullet-points into WA-ready check-lists and timing hacks.

Note on scope (from IPY3 → H2 bridge):
Some schools defer "equations of motion" until H1/H2 and emphasise graphical analysis only. This guide integrates IP Year 3 Chapter 2: Kinematics with H2 Topic 3: Motion & Forces so you can revise coherently either way.

3.1 Kinematics warm-up — language matters (merged from IPY3 Ch.2)

What this module covers (IPY3 Chapter 2 headings)

• 2.1 Speed, velocity and acceleration
• 2.2 Graphical analysis
• 2.3 Free fall
• 2.4 Equations of motion (SUVAT)

Key objectives (IP-friendly checklist)

1. State the difference between scalar and vector.
2. Define speed and velocity.
3. Compute average speed.
4. Define uniform acceleration and compute \( a = \dfrac{v-u}{t} \).
5. Interpret non-uniform (non-linear) acceleration examples.
6. Do data analysis (Y2Y3 math coordinate geometry).
7. Plot, deduce and interpret distance-time, speed-time, displacement-time, velocity-time graphs.
8. Use area under graph and gradient to calculate physical quantities.
9. State that near Earth's surface, free-fall acceleration is approximately \( 10\space \text{m}\space \text{s}^{-2} \) or \( 9.81\space \text{m}\space \text{s}^{-2} \), and is approximately constant.
10. Describe free fall (idealised: without air resistance).
11. Use the SUVAT equations to solve problems.

Terms you must be fluent with

Mnemonic: Dis-place-ment starts with D and P -> Direction and Position. Exam setters love swapping "distance" and "displacement".

Scalar, vector and diagrams

• A scalar has magnitude only.
• A vector has magnitude and direction.
• Distance is scalar; displacement is vector.
• Draw vectors as arrows (tip-tail); arrow length is proportional to magnitude; arrowhead shows direction.

Speed, velocity, acceleration (instantaneous vs average)

• Speed: rate of change of distance at an instant.
• Velocity: rate of change of displacement at an instant.
• Average speed \( = \dfrac{\text{total distance}}{\text{total time}} \).
• Average velocity \( = \dfrac{\text{total displacement}}{\text{total time}} \).
• Acceleration: rate of change of velocity at an instant.
• Average acceleration \( = \dfrac{\Delta v}{\Delta t} \).

Graph-first link: Units and graph axes hint which tool to use: gradient -> derivative (slope), area -> integral (accumulated change).

3.2 Graphical analysis — s-t, v-t, a-t (with exemplars)

3.2.1 Displacement-Time (s-t)

Meaning: how position changes with time.
Key features

• Slope = velocity.
• Straight line (constant slope) -> uniform velocity.
• Curved line -> non-uniform velocity.
• Horizontal line -> at rest.

Typical diagrams

• Straight upward line -> constant positive velocity.
• Curve getting steeper -> increasing velocity (acceleration).
• Curve flattening -> decreasing velocity (deceleration).

3.2.2 Velocity-Time (v-t)

Meaning: how velocity changes with time.
Key features

• Slope = acceleration.
• Area under curve = displacement.
• Horizontal line -> constant velocity.
• Straight sloping line -> uniform acceleration/deceleration.
• Curved line -> non-uniform acceleration.

IP hack: Photocopy one v-t diagram with five different slopes and areas; annotate ( s ) (area) and ( a ) (slope) for each. Spend 3 minutes every Sunday redrawing from memory until Prelims.

Canonical cases (with pictures)

• Constant velocity — \( v = 10\space \text{m}\space \text{s}^{-1} \) for 10 s; line is horizontal (zero acceleration).

• Constant acceleration — start from rest, \( a = 2\space \text{m}\space \text{s}^{-2} \) for 10 s; straight line with positive slope.

• Constant deceleration — start at \( 20\space \text{m}\space \text{s}^{-1} \), \( a = -2\space \text{m}\space \text{s}^{-2} \), stop after 10 s; straight line with negative slope.

• Rest — \( v = 0 \) for 10 s; horizontal at \( y = 0 \).

• Accelerate then decelerate — rise to \( 10\space \text{m}\space \text{s}^{-1} \) by \( t = 5\space \text{s} \), then back to \( 0 \) by \( t = 10\space \text{s} \); triangular (often approximated quadratic) shape.

• Negative velocity with constant acceleration — moving in negative direction at \( -10\space \text{m}\space \text{s}^{-1} \), \( a = -2\space \text{m}\space \text{s}^{-2} \); straight line with negative slope (velocity becomes more negative).

3.2.3 Acceleration-Time (a-t)

Meaning: how acceleration changes with time.
Key features

• Horizontal line -> constant acceleration.
• Slope -> rate of change of acceleration (jerk).
• Area under curve -> change in velocity.

Canonical cases (with pictures)

• Constant acceleration — \( a = 2\space \text{m}\space \text{s}^{-2} \); horizontal line at \( a = 2 \).

• Zero acceleration — constant velocity; horizontal at \( a = 0 \).

• Step change — from \( 0 \) to \( 3\space \text{m}\space \text{s}^{-2} \) at \( t = 5\space \text{s} \) (e.g., rocket ignition).

• Negative constant acceleration — \( a = -2\space \text{m}\space \text{s}^{-2} \); horizontal below time axis.

3.2.4 How the three graphs talk to each other

• From s-t, gradient -> velocity.
• From v-t, gradient -> acceleration, area -> displacement.
• From a-t, area -> change in velocity.

These fall out of coordinate geometry and units. Axes units often tell you whether slope or area recovers the desired quantity.

Side-by-side comparison

• Uniform motion: straight s-t; constant v; zero a.
• Uniform acceleration: curved s-t; straight rising v-t; constant \( a>0 \).
• Uniform deceleration: s-t curve flattens; straight falling v-t; constant \( a<0 \).

3.3 Free fall (idealised: no air resistance)

3.3.1 Definition

• Motion under gravity alone; neglect air resistance.
• Near Earth's surface, take \( g \approx 9.81\space \text{m}\space \text{s}^{-2} \) (often \( 10\space \text{m}\space \text{s}^{-2} \) in quick estimates), direction downwards.

3.3.2 Key motion patterns

• Dropped object: \( u = 0 \), accelerates downward at \( +g \) (choose sign convention consistently).
• Thrown upwards: \( u>0 \) upward, acceleration still \( -g \); slows to \( v=0 \) at peak, then speeds up downward.

3.4 SUVAT — five equations for uniform acceleration

Uniform straight-line motion with constant acceleration gives the classic SUVAT equations:

\[ \begin{array}{l c} \text{No displacement }&s& \hspace{5em} & v & = & u + at \hspace{10em} \[6pt] \text{No initial velocity }&u& \hspace{5em} & s & = & vt - \tfrac12 at^2 \hspace{10em} \[6pt] \text{No final velocity }&v& \hspace{5em} & s & = & ut + \tfrac12 at^2 \hspace{10em} \[6pt] \text{No acceleration }&a& \hspace{5em} & s & = & \tfrac12(u + v)t \hspace{10em} \[6pt] \text{No time }&t& \hspace{5em} & v^2 & = & u^2 + 2as \hspace{10em} \end{array} \]

Why they work: just the definitions of velocity \( v \) and acceleration \( a \) plus areas under a v-t graph (triangles and rectangles).

3.4.1 The one-look flow chart

1. List \( s, u, v, a, t \).
2. Cross out the quantity not given.
3. Pick the single equation that omits that quantity. (No simultaneous equations, no tears.)

3.4.2 Simplified examples

• Drop from rest: \( u=0 \); \( v = g t \); \( s = \tfrac{1}{2} g t^{2} \).
• Throw up at 20 m s^-1 (use \( g=10\space \text{m}\space \text{s}^{-2} \) for mental math):
  • Time to peak: \( t_\text{up} = \dfrac{u}{g} = 2\space \text{s} \).
  • Max height: \( s_\text{max} = \dfrac{u^{2}}{2 g} = \dfrac{20^{2}}{20} = 20\space \text{m} \).
  • Total flight time: \( 2u/g = 4\space \text{s} \).

Exam reality check: Don't expect every value to be given explicitly. Many are inferred from graphs, units, or geometric areas; often you compute an intermediate quantity first.

3.5 Mass and inertia — why bowling balls don't dodge

Mass is the built-in stubbornness against acceleration. The larger the mass, the larger the reluctance to change velocity.

Class demo: roll a tennis ball vs a bowling ball with the same push; compare how quickly each slows — the difference is inertia made visible.

3.6 Linear momentum — the motion coin

\( \vec p = m \vec v \).
A vector conserved in closed systems; central to collision questions.

Mini-drill: Two carts: \( 2\space \text{kg} \) at \( +3\space \text{m}\space \text{s}^{-1} \) and \( 1\space \text{kg} \) at \( -2\space \text{m}\space \text{s}^{-1} \). Compute total \( \vec p \) before and after elastic and inelastic interactions; momentum matches even when KE is lost (inelastic).

3.7 Newton's trilogy (with teaching tips)

3.7.1 Common 3rd-law misconception (force pairs)

Students often pair forces incorrectly on FBDs. For a box on a table:

• The reaction to the box's weight \( W_\text{box} \) (Earth pulls box) is the box's gravitational pull on Earth.
• It is not the table's normal on the box; that normal pairs with the box's push on the table.

3.8 Vector diagrams — tip-to-tail never fails

Add forces graphically: draw the first vector; place the tail of the next at the tip of the previous; the resultant runs from the original tail to the final tip.

Student challenge: Put an object on an incline; resolve weight into \( m g \sin\theta \) (down-slope) and \( m g \cos\theta \) (perpendicular). Use \( F = m a \) for the acceleration; then a SUVAT equation to find time to slide 2 m.

3.9 Three WA timing rules (Motion edition)

1. Spend 30 s sketching the right diagram before touching equations.
2. Highlight given variables — prevents mixing up \( u \) and \( v \).
3. For "show that" proofs, copy the target first; work backwards to the single SUVAT that gets you there.

3.10 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Khan Academy — Distance vs. displacement
• Velocity-Time Graphs — Khan Academy
• Kinematic Equations — The Physics Classroom
• Deriving suvat — The Chalkface PDF
• Inertia & Mass — The Physics Classroom
• Momentum (Wikipedia)
• Newton's Laws — NASA Glenn
• Free Fall — Lumen Learning
• Tip-to-Tail Method — PhysicsThisWeek

3.11 Call-to-action

Parents: schedule a 1-h Motion & Forces clinic two weeks before WA 1; we cover graph reading, SUVAT drills and Newton's Laws MCQs.
Students: print this post, fold to A5, stick inside your formula booklet — revisit every bus ride.

Last updated 14 Jul 2025. Next review after SEAB releases the 2027 draft syllabus.