This mini-lesson walks you through the whole of OCR Gateway Topic P2 — Forces: P2.1 Motion (speed, velocity, acceleration, graphs and v²=u²+2as), P2.2 Newton's Laws (resultant forces, F=ma, momentum and work done) and P2.3 Forces in action (Hooke's law, weight, moments and pressure in fluids).
Make a guess: what does the slope of a speed–time graph show?
Mission 1How can one line tell the whole journey?
Mission 2Same push: why do the trolleys differ?
Mission 3What pushes the cannon backwards?
Mission 4Why won't the spring spring back?
Mission 5Why does a longer spanner work better?
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Higher-tier-only ideas are flagged. Press Start when you're ready.
P2.1 · Scalars & vectors
Two kinds of quantity
Every quantity in P2 is either a scalar or a vector:
Scalar — has size only. Examples: distance, speed, mass, time, energy.
Vector — has size and direction. Examples: displacement, velocity, acceleration, force, weight, momentum.
Distance is how far you actually travel; displacement is the straight-line distance and direction from start to finish.
Watch out: a car going round a roundabout at a steady 30 km/h has constant speed but a changing velocity — its direction keeps changing, so the vector changes.
Quick check
Scalar or vector?
?Which of these is a vector quantity?
P2.1 · Speed
Speed = distance ÷ time
For uniform motion, distance, speed and time are linked by:
s = v tdistance (m) = speed (m/s) × time (s)
You should know some typical everyday speeds to sanity-check answers:
Walking ≈ 1.5 m/s
Running ≈ 3 m/s
Cycling ≈ 6 m/s
A car in a town ≈ 13 m/s (about 30 mph)
For motion that isn't uniform, use the average speed = total distance ÷ total time. The speed of sound in air is about 330 m/s; wind speeds vary with the weather.
Calculate
Your turn — speed
1A runner covers 400 m in 50 s at a steady pace. Calculate their average speed.
m/s
Hint: v = distance ÷ time = 400 ÷ 50.
P2.1 · Acceleration
Acceleration & the velocity–time graph
Acceleration is how quickly velocity changes:
a = Δv ÷ tacceleration (m/s²) = change in velocity (m/s) ÷ time taken (s)
On a velocity–time graph the gradient is the acceleration, and the area under the line is the distance travelled:
Here velocity rises from 0 to 20 m/s in 10 s, so a = 20 ÷ 10 = 2 m/s² (the gradient). Distance = area of the triangle = ½ × 10 × 20 = 100 m.
HigherFor a curved velocity–time graph the acceleration changes; you can still find the distance from the area under the curve, and the acceleration at a point from the gradient of the tangent.
Calculate
Your turn — acceleration
2A cyclist speeds up from 4 m/s to 16 m/s in 6 s. Calculate their acceleration.
m/s²
Hint: a = (16 − 4) ÷ 6.
Mission 1 check
How can one line tell the whole journey?
?A graph of speed against time shows a car braking. The line falls in a straight line from 20 m/s to 0 m/s in 4 s. How hard did it brake?
P2.1 · Uniform acceleration
The uniform-acceleration equation
When acceleration is constant, this equation links the velocities, acceleration and distance — no time needed:
Here u = starting velocity, v = final velocity, a = acceleration, s = distance.
Worked example
A train starts from rest (u = 0) and accelerates at 0.5 m/s² over 400 m.
v² = 0² + 2 × 0.5 × 400 = 400, so v = √400 = 20 m/s
Free-fall: near Earth, objects accelerate downward at about 10 m/s² (9.8 m/s² to one decimal place) when air resistance is ignored.
Calculate
Your turn — v² = u² + 2as
3A car starts from rest and accelerates at 3 m/s² over a distance of 24 m. Calculate its final velocity.
m/s
Hint: v² = 0² + 2 × 3 × 24 = 144, then take the square root.
Mission 2 of 5
Same push: why do the trolleys differ?
Make a guess: why does the same push move them so differently?
P2.2 · Resultant forces
Resultant forces & free-body diagrams
Objects interact by contact forces (friction, normal contact) and non-contact forces (gravity, magnetism, electrostatic). A free-body diagram shows every force on one object as an arrow. Add forces along a line to get the resultant:
Up/down balance (500 N each). Horizontally: 500 N − 300 N = a resultant of 200 N forwards, so the box accelerates that way.
HigherForces that aren't in a line can be added with a scale vector diagram to find the resultant; when forces balance to zero the object is in equilibrium.
P2.2 · Newton's three laws
Newton's laws of motion
First law: an object stays still, or moves at constant velocity, unless a resultant force acts on it.
Second law: a resultant force causes acceleration — F = m a (bigger force or smaller mass → bigger acceleration).
Third law: when two objects interact they exert equal and opposite forces on each other.
F = m aresultant force (N) = mass (kg) × acceleration (m/s²)
Watch out: the first law is the one people get wrong — an object moving at steady speed in a straight line has balanced forces (zero resultant). You do not need a forward force to keep something moving, only to change its motion.
Quick check
Reading the forces
?A lorry drives along a motorway at a constant 25 m/s in a straight line. What can you say about the forces on it?
Calculate
Your turn — F = ma
4A resultant force acts on a 1500 kg car, giving it an acceleration of 2 m/s². Calculate the size of the resultant force.
N
Hint: F = m × a = 1500 × 2.
Mission 2 check
Same push: why do the trolleys differ?
?A 1000 kg car and a 3000 kg van are each pulled with the same resultant force of 3000 N. Which statement is correct?
P2.2 / P2.3 · Weight
Weight, mass & inertia
Mass (kg) is the amount of matter in an object — it's the same everywhere. Weight (N) is the force of gravity on that mass:
W = m gweight (N) = mass (kg) × gravitational field strength (N/kg)
On Earth g ≈ 10 N/kg (9.8 N/kg to one decimal place; OCR exam questions use 10). On the Moon g is only about 1.6 N/kg, so the same mass weighs less there.
Watch out: weight and mass are not the same! Mass never changes; weight depends on the gravitational field. HigherInertial mass measures how hard it is to change an object's velocity — it is the ratio force ÷ acceleration (m = F/a).
Calculate
Your turn — weight
5A bag of shopping has a mass of 4 kg. Using g = 10 N/kg, calculate its weight on Earth.
N
Hint: W = m × g = 4 × 10.
Mission 3 of 5
What pushes the cannon backwards?
Make a guess: why does the cannon roll backwards?
P2.2 · Momentum · Higher tier
Momentum & its conservation
Every moving object has momentum — a vector that depends on mass and velocity:
p = m vmomentum (kg·m/s) = mass (kg) × velocity (m/s)
In a closed system (no external resultant force), the total momentum before a collision or explosion equals the total momentum after — this is the conservation of momentum.
Before: 2×3 + 1×0 = 6 kg·m/s. After: 3 kg × 2 m/s = 6 kg·m/s. Momentum is conserved.Calculate
Your turn — momentum
6A 1200 kg car travels at 15 m/s. Calculate its momentum.
kg·m/s
Hint: p = m × v = 1200 × 15.
Mission 3 check
What pushes the cannon backwards?
?A skater stands still on smooth ice, holding a heavy ball. She throws the ball forwards. What happens to her, and why?
P2.2 · Work done
Work done by a force
When a force moves an object along its line of action, it does work — transferring energy from one store to another:
W = F swork done (J) = force (N) × distance moved along the line of the force (m)
One joule is the work done when a force of 1 N moves an object 1 m (1 J = 1 N·m). Doing work against friction warms the surfaces up.
Worked example
A cleaner pushes a trolley with a force of 40 N over 6 m.
W = F × s = 40 × 6 = 240 J
Calculate
Your turn — work done
7A force of 250 N drags a sledge 12 m across the snow. Calculate the work done.
J
Hint: W = F × s = 250 × 12.
Mission 4 of 5
Why won't the spring spring back?
Make a guess: why does the spring stay stretched?
P2.3 · Elasticity · PAG P2
Hooke's law & elastic energy
Stretch a spring and the force needed is proportional to the extension — Hooke's law:
F = k eforce (N) = spring constant (N/m) × extension (m)
Force ∝ extension only up to the limit of proportionality (the straight part). The area under the line is the elastic energy stored.
E = ½ k e²elastic energy stored (J) = ½ × spring constant (N/m) × extension² (m²)
Elastic vs inelastic: after elastic deformation an object returns to its original shape; after plastic (inelastic) deformation it stays bent. Practical (PAG P2): hang masses on a spring, measure extension, and plot force against extension to find k from the gradient.
Calculate
Your turn — Hooke's law
8A spring has a spring constant of 50 N/m. What force is needed to stretch it by an extension of 0.30 m?
N
Hint: F = k × e = 50 × 0.30.
Mission 4 check
Why won't the spring spring back?
?A student hangs more and more weights on a spring. After the last one, she removes them all. The spring is now 2 cm longer than at the start. What has happened?
Calculate
Your turn — elastic energy
9The same spring (k = 50 N/m) is stretched by an extension of 0.30 m. Calculate the elastic energy stored.
J
Hint: E = ½ × 50 × 0.30². (0.30² = 0.09)
Mission 5 of 5
Why does a longer spanner work better?
Make a guess: why does the longer spanner turn the nut?
P2.3 · Moments
Moments — the turning effect
A force can turn an object about a pivot. The moment measures this turning effect:
M = F dmoment (N·m) = force (N) × perpendicular distance from pivot (m)
When something balances, the total clockwise moment = total anticlockwise moment (the principle of moments):
Anticlockwise: 400 × 1.5 = 600 N·m. Clockwise: 300 × 2.0 = 600 N·m. They are equal, so the beam balances.
Watch out: the distance in M = Fd is the perpendicular distance from the pivot to the line of the force. Levers and gears work as force multipliers — a long lever (or a large gear) turns a small force into a big moment.
Calculate
Your turn — moments
10A spanner is used to undo a nut. A force of 60 N is applied at a perpendicular distance of 0.25 m from the nut. Calculate the moment.
N·m
Hint: M = F × d = 60 × 0.25.
Mission 5 check
Why does a longer spanner work better?
?A stuck nut needs a moment of 60 N m to turn. Jo pushes at right angles with 200 N on a 0.25 m spanner, but it won't move. With a 0.40 m spanner and the same push, it turns. Why?
P2.3 · Pressure in fluids
Pressure & hydraulics
A fluid (a gas or liquid) presses on every surface it touches, at right angles to that surface. Pressure spreads a force over an area:
p = F ÷ Apressure (Pa) = force normal to surface (N) ÷ area (m²)
The same force over a smaller area gives a bigger pressure — which is why a drawing pin's sharp point pierces a board while your flat thumb does not.
In a hydraulic system the pressure is the same throughout, so a small force on a small piston produces a large force on a large one.
Boundary note: in OCR Gateway, pressure with depth in a liquid (p = hρg), upthrust and floating sit in P1 Matter; in P2.3 you need p = F/A and how hydraulic systems use it.
Quick check
Force, area & pressure
?Why does a sharp knife cut more easily than a blunt one when you push with the same force?
Sort it
Scalar or vector?
Tap a quantity, then tap the box it belongs in.
📏 Scalar
🧭 Vector
Recap
The equations to know
Speed: s = v t · Acceleration: a = Δv ÷ t
Uniform acceleration: v² = u² + 2 a s
Newton's 2nd law: F = m a · Weight: W = m g
Momentum (HT): p = m v
Work done: W = F s
Hooke's law: F = k e · Elastic energy: E = ½ k e²
Moment: M = F d · Pressure: p = F ÷ A
You've covered the key ideas across the three parts of OCR Gateway P2 — motion, Newton's laws, and forces in action. Press Finish to see your score.
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Mini-lesson complete!
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You've worked through Forces for OCR Gateway GCSE Physics. 🎉