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, weight and momentum) and P2.3 Forces in action (work done, Hooke's law, moments and pressure in fluids).
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.
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 9.8 m/s² (often rounded to 10) 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.
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.
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 ≈ 9.8 N/kg (often rounded to 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 = 9.8 N/kg, calculate its weight on Earth.
N
Hint: W = m × g = 4 × 9.8.
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.
P2.3 · 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.
P2.3 · Elasticity · required practical
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 inelastic (plastic) deformation it stays bent. Required practical: 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.
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)
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.
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 all three parts of OCR Gateway P2 — motion, Newton's laws, and forces in action. Press Finish to see your score.
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