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.
Concrete example: how to use this page
If a question gives a velocity-time graph, read gradients and areas before reaching for equations. If it gives constant acceleration data in words, then use the SUVAT equations. Choosing the representation first removes most motion-topic confusion.
Motion route-selection map
Use this map before choosing equations. Most errors in this topic come from forcing every question into SUVAT too early.
Question cue
First move
Equation or check
Common trap
Displacement-time, velocity-time, or acceleration-time graph
Read the axes and units before calculating.
Gradient gives the rate; area gives the accumulated change.
Using a graph formula without checking whether the graph is s-t, v-t, or a-t.
Constant acceleration in words
List s,u,v,a,t
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, then cross out the missing quantity.
Pick the SUVAT equation that omits the missing variable.
Using SUVAT when acceleration is changing.
Free fall or vertical throw
Choose upward or downward as positive and keep it consistent.
Acceleration is always g downward near Earth's surface.
Setting acceleration to zero at the highest point.
"Resultant force", lift, slope, or connected bodies
Draw the free-body diagram before writing Newton's second law.
Use ∑F=ma along chosen axes.
Using a single force instead of the resultant force.
Collision, carts, or explosion
Define the system and direction before comparing before and after.
Total momentum is conserved for an isolated system.
Expecting kinetic energy to be conserved in every collision.
Bookmark the H2 Physics notes hub to jump straight into the neighbouring circular-motion, energy, and oscillations chapters once you finish this topic.
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)
Read the gradient before reading the height of an s-t graph. The height tells you displacement from the chosen origin; the gradient tells you velocity.
Graph feature
Motion meaning
What to write
Common trap
Straight line with positive gradient
Constant velocity in the positive direction
Steeper positive gradient means larger speed in the positive direction.
Saying the object is faster just because it is higher on the graph.
Straight line with negative gradient
Constant velocity in the negative direction
The speed is the size of the gradient; the velocity is negative.
Saying the speed itself is negative.
Horizontal line
Zero velocity
The object is at rest even if its displacement is not zero.
Saying zero velocity means zero displacement.
Curve getting steeper
Velocity magnitude is increasing
Draw a tangent if an instantaneous velocity is needed.
Using the average gradient for one instant.
Curve flattening
Velocity magnitude is decreasing
The tangent gradient is getting smaller in magnitude.
Saying acceleration is zero just because displacement is still changing.
Worked check: a line from s=0 to s=20m in 4s has velocity 5m⋅s−1. A line from s=20m to s=4m in 4s has velocity −4m⋅s−1. The first has the larger speed; the second has negative velocity.
Misconception check: area under an s-t graph is not the useful graph tool here. Use gradient for velocity, then switch to v-t graphs when you need displacement from area.
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.
Velocity-time signed-area checkpoint
When a velocity-time graph crosses the time axis, split the graph into regions before adding areas.
Region on the graph
Meaning
How to use the area
Common trap
Above the time axis
Motion in the positive direction
Add this area for signed displacement.
Calling it total distance without checking for negative regions.
Below the time axis
Motion in the negative direction
Subtract this area for signed displacement.
Ignoring the sign and overestimating displacement.
Total distance travelled
Actual path length
Add the magnitudes of all regions.
Cancelling areas when the question asks for distance.
Worked check: if a cart has 12m of positive area and 5m of negative area, its displacement is 7m in the positive direction, but its total distance travelled is 17m.
Misconception check: area below the time axis is not "negative distance". It is negative displacement because velocity has a direction.
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 displacement (s): v=u+at
No initial velocity (u): s=vt−21at2
No final velocity (v): s=ut+21at2
No acceleration (a): s=21(u+v)t
No time (t): v2=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 20m⋅s−1 (use g=10m⋅s−2 for mental math):
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 F=ma 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.
Need structured practice on Motion and Forces? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section I, Topic 3 Syllabus outcomes
Candidates should be able to:
(a) show an understanding of and use the terms position, distance, displacement, speed, velocity and acceleration.
(b) use graphical methods to represent distance, displacement, speed, velocity and acceleration.
(c) identify and use the physical quantities from the gradients of position-time or displacement-time graphs and areas under and gradients of velocity-time graphs, including cases of non-uniform acceleration.
(d) derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line.
(e) solve problems using equations which represent uniformly accelerated motion in a straight line, e.g. for bodies falling vertically without air resistance in a uniform gravitational field.
(f) show an understanding that mass is the property of a body which resists change in motion (inertia).
(g) define and use linear momentum as the product of mass and velocity.
(h) state and apply each of Newton's laws of motion (first, second, and third laws).
(i) recall the relationship resultant force F=ma for a body of constant mass, and use this to solve problems.
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
vˉ=ΔtΔs
Instantaneous velocity
v=dtds - area under an a-t graph gives Δv
SUVAT family
v=u+at, s=ut+21at2
Newton's 2nd law
F=ma
Friction (qualitative)
Contact force opposing relative motion or its tendency. 9478 requires qualitative treatment only; coefficients of friction are not in the syllabus.
Weight
W=mg
Resultant for circular motion link
a=rv2 - points to centre (preview of Topic 7)
Term guide
Symbol / term
Meaning
u
Initial velocity
v
Final or instantaneous velocity
vˉ
Average velocity over the interval
s
Displacement
a
Acceleration
t,Δt
Time / elapsed time
m
Mass
F
Resultant force vector
Ffric
Frictional force (qualitative; no coefficient of friction in 9478)
R
Normal reaction force
g
Gravitational field (acceleration due to gravity)
r
Radius of circular path
a=v2/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.
Last updated 14 Jul 2025. Next review after SEAB releases the 2027 draft syllabus.
