Q: What does A-Level Physics: 3) Motion & Forces Guide cover? A: From displacement graphs to Newton's three laws.
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)
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=10m⋅s−1 for 10 s; line is horizontal (zero acceleration).
Constant acceleration - start from rest, a=2m⋅s−2 for 10 s; straight line with positive slope.
Constant deceleration - start at 20m⋅s−1, a=−2m⋅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 10m⋅s−1 by t=5s, then back to 0 by t=10s; triangular (often approximated quadratic) shape.
Negative velocity with constant acceleration - moving in negative direction at −10m⋅s−1, a=−2m⋅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=2m⋅s−2; horizontal line at a=2.
Zero acceleration - constant velocity; horizontal at a=0.
Step change - from 0 to 3m⋅s−2 at t=5s (e.g., rocket ignition).
Negative constant acceleration - a=−2m⋅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.
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:
No displacementsv=u+atNo initial velocityus=vt−21at2No final velocityvs=ut+21at2No accelerationas=21(u+v)tNo timetv2=u2+2as
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
List s,u,v,a,t.
Cross out the quantity not given.
Pick the single equation that omits that quantity. (No simultaneous equations, no tears.)
3.4.2 Simplified examples
Drop from rest: u=0; v=gt; s=21gt2.
Throw up at 20 \pu{m.s-1} (use g=10m⋅s−2 for mental math):
Time to peak: tup=gu=2s
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
p=mv. A vector conserved in closed systems; central to collision questions.
Mini-drill: Two carts: 2kg at +3m⋅s−1 and 1kg at −2m⋅s−1. Compute total p before and after elastic and inelastic interactions; momentum matches even when KE is lost (inelastic).
3.7 Newton's trilogy (with teaching tips)
Law
Exam-level phrasing
Teaching tip
1
A body remains at rest or uniform velocity unless acted on by a resultant external force.
Use an air-track puck to visualise.
2
Resultant force is proportional to the rate of change of momentum, same direction.
Reduces to \( \vec F = m \vec a \) for constant mass.
3
Forces between two bodies are equal and opposite and act along the same line.
Balloon-rocket demo works.
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 weightWbox (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 mgsinθ (down-slope) and mgcosθ (perpendicular). Use F=ma for the acceleration; then a SUVAT equation to find time to slide 2 m.
3.9 Three WA timing rules (Motion edition)
Spend 30 s sketching the right diagram before touching equations.
Highlight given variables - prevents mixing up u and v.
For "show that" proofs, copy the target first; work backwards to the single SUVAT that gets you there.
Comprehensive revision pack
9478 Section I, Topic 3 Syllabus outcomes at a glance
Outcome (a) - describe displacement, velocity and acceleration using calculus language.
Outcome (b) - interpret and sketch s-t, v-t and a-t graphs, extracting gradients and areas.
Outcome (c) - apply the equations of motion for constant acceleration and recognise their limits.
Outcome (d) - state and use Newton's three laws, including frictional and tension forces.
Outcome (e) - analyse motion in two dimensions (projectiles, relative velocity, circular motion bridge).
Concept map (in words)
Every question flows through Describe → Represent → Solve. Describe the motion verbally, represent it via graphs/free-body diagrams, then choose the correct tool: calculus integration/differentiation, SUVAT, or Newton's laws. Bridge constant-acceleration motion to dynamics by checking whether resultant forces are zero or not.
Key definitions & formulae
Item
Expression / highlight
Average velocity
\( \bar v = \dfrac{\Delta s}{\Delta t} \)
Instantaneous velocity
\( v = \dfrac{\mathrm{d}s}{\mathrm{d}t} \) — area under an a-t graph gives \( \Delta v \)
SUVAT family
\( v = u + at \), \( s = ut + \tfrac{1}{2} a t^{2} \), \( v^{2} = u^{2} + 2 a s \), \( s = \tfrac{(u + v)t}{2} \), \( s = v t - \tfrac{1}{2} a t^{2} \)
Newton's 2nd law
\( \vec F = m \vec a \)
Friction model
\( F_\text{fric} \le \mu_\text{s} R \) (static), \( F_\text{fric} = \mu_\text{k} R \) (kinetic)
Weight
\( \vec W = m \vec g \)
Resultant for circular motion link
\( a = \dfrac{v^{2}}{r} \) — points to centre (preview of Topic 7)
Term guide
Symbol / term
Meaning
\( u \)
Initial velocity
\( v \)
Final or instantaneous velocity
\( \bar v \)
Average velocity over the interval
\( s \)
Displacement
\( a \)
Acceleration
\( t, \Delta t \)
Time / elapsed time
\( m \)
Mass
\( \vec F \)
Resultant force vector
\( F_\text{fric} \)
Frictional force
\( \mu_\text{s}, \mu_\text{k} \)
Coefficients of static / kinetic friction
\( R \)
Normal reaction force
\( \vec g \)
Gravitational field (acceleration due to gravity)
\( r \)
Radius of circular path
\( a = v^2/r \)
Centripetal acceleration relation
Derivations & reasoning to master
SUVAT derivations from calculus: integrate constant acceleration to recover velocity and displacement equations.
Area-under-graph reasoning: prove displacement equals the area under a v-t curve using Riemann sums.
Newton's 2nd law → suvat: derive v2=u2+2as by combining F=ma with vdsdv.
Variable acceleration: practice using vdxdv or integrating a(t) when the acceleration isn't constant (common extension).
Worked example 1 - braking with reaction time
A car travels at 22m⋅s−1. The driver has a 0.80s reaction time before braking with constant deceleration 6.5m⋅s−2. Determine the total stopping distance.
Sketch solution: s=utreaction+utbrake−21atbrake2 with tbrake=au. Document reasoning with a v-t graph split into a reaction rectangle plus a braking triangle.
Worked example 2 - lift dynamics
A 75kg student stands on a scale in a lift accelerating downward at 1.8m⋅s−2. What reading does the scale show? What reading occurs if the lift cable snaps (free fall)?
Key idea: draw the FBD, write N−mg=ma. Solve for N. Discuss the limiting case (free fall → apparent weight zero).
Practical & data tasks
Use phone accelerometer apps to record motion along a corridor; export data and integrate numerically to recover displacement.
Construct ticker tape experiments; measure average acceleration and compare with v-t graph slopes.
Analyse an Atwood machine video frame-by-frame to practise resolving tension and acceleration simultaneously.
Common misconceptions & exam traps
Mixing up sign conventions when using suvat (define positive direction first).
Using a constant-acceleration equation when air resistance makes acceleration variable (state assumption).
Forgetting that velocity can be negative while speed is always positive.
Treating resultant force as an additional force arrow instead of the vector sum.
Quick self-check quiz
What does the gradient of a s-t graph represent? - Velocity.
Which suvat equation is independent of time? - v2=u2+2as.
A ball is thrown upward; at the top, what are v and a? - v=0,a=−g (downward).
State Newton's third law. - For every action there is an equal and opposite reaction.
How can you tell from a v-t graph that motion is in the opposite direction? - Velocity values become negative (below time axis).
Revision workflow
Complete a mixed set of 10 suvat problems (varied contexts) without notes; mark against solutions.
Reproduce the derivation of v2=u2+2as from scratch once a week.
Practise translating word problems into v-t sketches before writing equations.
Build a flashcard deck of standard acceleration profiles (free fall, lift, Atwood, projectile components) and test yourself daily.
Practice Quiz
Test yourself on the key concepts from this guide.
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.
