Edexcel International GCSE Physics (4PH1) · Section 1 — Forces and motion
Mini-Lesson
Forces & Motion
This mini-lesson walks you through the whole of Edexcel International GCSE (4PH1) Section 1 — Forces and motion: units, motion graphs, the equations of motion, the forces that change motion, Hooke's law, and the Paper-2 ideas of momentum and moments.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.
Units · 1.1 & 1.2P
The units examiners expect
Section 1 begins with the SI units you must use. Get these wired in now and every calculation later just works.
mass — kilogram (kg)
distance — metre (m)
speed / velocity — metre/second (m/s)
acceleration — metre/second² (m/s²)
force / weight — newton (N)
time — second (s)
gravitational field strength — newton/kilogram (N/kg)
Paper 2 only (1.2P): the newton metre (N m) for the moment of a force, and kilogram metre/second (kg m/s) for momentum. We meet both later.
Movement & position · 1.3, 1.4
Speed and distance–time graphs
On a distance–time graph, a steeper line means faster motion. A horizontal line means the object is stationary (distance not changing). The gradient gives the speed.
average speed = distance ÷ time
v = s ÷ t · measured in m/s
Required practical (1.5): investigate the motion of everyday objects such as toy cars or tennis balls — measure distance with a ruler/tape and time with a stopwatch or light gates, then calculate average speed.
Movement & position · 1.6
Acceleration is change of velocity
Acceleration tells you how quickly velocity changes. Speeding up is positive; slowing down (deceleration) is negative.
a = (v − u) ÷ t
a = acceleration (m/s²) · v = final velocity · u = initial velocity (m/s) · t = time (s)
Worked example
A cyclist speeds up from u = 4 m/s to v = 16 m/s in t = 6 s.
a = (16 − 4) ÷ 6 = 12 ÷ 6 = 2 m/s²
Misconception: acceleration is a change in velocity, not just speed. A car going round a roundabout at constant speed is still accelerating because its direction (and so its velocity) is changing.
Your turn
Calculate the acceleration
?A train accelerates from u = 6 m/s to v = 30 m/s in 8 s. Work out its acceleration in m/s².
m/s²
a = (v − u) ÷ t = (30 − 6) ÷ 8
Movement & position · 1.7–1.9
Velocity–time graphs
This is the graph examiners love. Read it two ways:
Ramp 0→12 m/s in 4 s, then steady at 12 m/s to 10 s. Gradient = acceleration = 3 m/s²; area under the line = distance = 24 + 72 = 96 m.
Gradient of the line = acceleration (1.8). A flat line means zero acceleration — constant velocity.
Area between the line and the time axis = distance travelled (1.9).
Your turn
Read the velocity–time graph
?Using the graph above, what total distance does the object travel in the full 10 s? (Add the triangle and the rectangle.)
m
triangle ½·4·12 = 24 m, plus rectangle 6·12 = 72 m
Movement & position · 1.10
When there is no time given
Sometimes a problem links final speed, initial speed, acceleration and distance — but gives you no time. This equation is for exactly that:
A ball starts from rest (u = 0) and accelerates at a = 3 m/s² over s = 24 m.
v² = 0² + (2 × 3 × 24) = 144
v = √144 = 12 m/s
Your turn
Use v² = u² + 2as
?A car travelling at u = 8 m/s accelerates at a = 2 m/s² over a distance of s = 33 m. Find its final speed v, in m/s.
m/s
v² = 8² + 2×2×33 = 64 + 132 = 196, then v = √196
Forces & movement · 1.11–1.16
Forces, vectors and the resultant
A force can change an object's speed, shape or direction (1.11). Forces come in types — e.g. gravitational, electrostatic, friction, contact (1.12).
Force is a vector — it has size and direction (1.14) — unlike a scalar such as mass or time, which has size only (1.13). When forces act along a line, add the ones pointing one way and subtract the others to get the resultant force (1.15).
Horizontal resultant = 400 − 250 = 150 N forward, so the car accelerates forwards. Vertically, normal (600 N) and weight (600 N) are balanced, so it stays on the road.
Friction (1.16): friction is a force that opposes motion — it always acts against the direction an object is moving or trying to move.
Quick check
Balanced or not?
?A lorry drives along a straight, flat road at a steady 20 m/s. What must be true of the forces on it?
Forces & movement · 1.17
Newton's second law: F = m a
An unbalanced (resultant) force makes a mass accelerate. The bigger the force, the bigger the acceleration; the bigger the mass, the smaller the acceleration.
F = m × a
force (N) = mass (kg) × acceleration (m/s²)
Worked example
A 1500 kg car has a resultant force of 4500 N.
a = F ÷ m = 4500 ÷ 1500 = 3 m/s²
Your turn
Use F = m a
?A 1200 kg car accelerates at 2.5 m/s². What resultant force is needed, in newtons?
N
F = m × a = 1200 × 2.5
Forces & movement · 1.18
Weight is a force
Weight is the pull of gravity on a mass. It is measured in newtons, not kilograms.
W = m × g
weight (N) = mass (kg) × gravitational field strength (N/kg) · on Earth g ≈ 10 N/kg
Misconception — weight vs mass:mass (kg) is the amount of matter and is the same everywhere. Weight (N) depends on g, so the same astronaut weighs less on the Moon (g ≈ 1.6 N/kg) even though their mass is unchanged.
Your turn
Calculate the weight
?A school bag has a mass of 8 kg. Taking g = 10 N/kg, what is its weight on Earth, in newtons?
N
W = m × g = 8 × 10
Forces & movement · 1.19–1.21
Stopping distance & terminal velocity
Stopping distance of a vehicle is the sum of two parts (1.19):
stopping distance = thinking distance + braking distance
thinking = distance during the driver's reaction time · braking = distance while the brakes act
Thinking distance grows with speed and reaction time (tiredness, alcohol, distraction).
Braking distance grows with speed, greater mass, and worse road/tyre condition (wet or icy) (1.20).
Terminal velocity (1.21): a falling object speeds up, so air resistance grows. When air resistance balances weight, the resultant force is zero and the object falls at a constant terminal velocity.
Changing shape · 1.22–1.24
Hooke's law & the spring practical
Stretch a spring and its extension is proportional to the force — up to a point.
F = k × x
force (N) = spring constant (N/m) × extension (m)
The straight, linear region obeys Hooke's law (1.23): here every 0.20 m of extension needs 4 N, so k = 4/0.20 = 20 N/m. Past the limit of proportionality the line curves.
Practical (1.22): hang masses on helical springs, metal wires and rubber bands and measure extension. Elastic behaviour (1.24) = the material returns to its original shape once the force is removed.
Your turn
Use F = k x
?A spring has a spring constant k = 25 N/m. What force is needed to stretch it by an extension of x = 0.20 m? Give your answer in newtons.
N
F = k × x = 25 × 0.20
Momentum · 1.25P–1.28P · Paper 2 only
Momentum (Paper 2 / Physics)
Momentum measures how hard a moving object is to stop. It is a vector.
p = m × v
momentum (kg m/s) = mass (kg) × velocity (m/s)
In a collision or explosion with no external force, the total momentum is conserved (1.27P): total before = total after. That idea underpins safety features — crumple zones, airbags and seatbelts increase the time a collision takes, which reduces the force (1.26P):
F = (mv − mu) ÷ t
force (N) = change in momentum ÷ time taken
Paper 2 only
Calculate the momentum
?A 1500 kg car travels at 12 m/s. What is its momentum, in kg m/s?
kg m/s
p = m × v = 1500 × 12
Moments · 1.29P–1.33P · Paper 2 only
Moments & balance (Paper 2 / Physics)
A moment is the turning effect of a force about a pivot.
moment = force × perpendicular distance from the pivot
moment (N m) = force (N) × distance (m)
Anticlockwise moment = 40 × 1.5 = 60 N m. Clockwise moment = 30 × 2.0 = 60 N m. They are equal, so the beam balances — the principle of moments (1.32P).
The principle of moments (1.32P): for a balanced object, total clockwise moment = total anticlockwise moment. The weight of a body acts through its centre of gravity (1.31P), and how the upward support forces on a beam change as a heavy object is moved along it is examined under 1.33P. Newton's third law (1.29P) reminds us forces come in equal, opposite pairs on different bodies.
Misconception: a moment uses the perpendicular distance from the pivot to the line of the force — not the length of the object or a slanted distance.
Paper 2 only
Make the seesaw balance
?A child of weight 600 N sits 2.0 m to the left of a pivot. A second child sits 3.0 m to the right. What weight makes the seesaw balance?
Quick check
Vector or scalar?
?A car drives around a roundabout at a constant speed of 10 m/s. Which statement is correct?
Recap
The Section 1 toolkit
Every equation and idea from 4PH1 Section 1 in one place:
Speed: v = s ÷ t
Acceleration: a = (v − u) ÷ t
v–t graph: gradient = acceleration · area = distance
No time given: v² = u² + (2 × a × s)
Newton's 2nd law: F = m × a
Weight: W = m × g
Hooke's law: F = k × x (linear region)
Stopping distance: thinking + braking
Momentum (P2): p = m × v · F = (mv − mu) ÷ t
Moments (P2): moment = force × perpendicular distance
You've covered the whole of Edexcel iGCSE Physics (4PH1) Section 1 — Forces and motion, including the Paper-2 momentum and moments content. Press Finish to see your score.
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