Forces and Motion

This guide covers Topic 1, Forces and motion, in full — sub-topics (a) Units, (b) Movement and position and (c) Forces, movement, shape and momentum — from the Pearson Edexcel International GCSE in Physics (4PH1), Issue 4 specification (first teaching September 2017, current from September 2024). Statements marked with a “P” reference in the official specification are Physics-only content, not shared with the International GCSE in Science (Double Award), and are noted as such below.

Before studying this

This is the first topic of the specification and assumes no prior physics study beyond general numeracy and basic graph-reading skills.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL GCSE PHYSICS (4PH1) — Topic 1

(a) Units — using the units kilogram (kg), metre (m), metre/second (m/s), metre/second² (m/s²), newton (N), second (s) and newton/kilogram (N/kg); [P] also using newton metre (Nm) and kilogram metre/second (kg m/s).

(b) Movement and position — plotting and explaining distance-time graphs; knowing and using average speed = distance moved / time taken; investigating the motion of everyday objects practically; knowing and using acceleration = change in velocity / time taken; plotting and explaining velocity-time graphs; determining acceleration from the gradient of a velocity-time graph; determining distance travelled from the area under a velocity-time graph; using v² = u² + 2as.

(c) Forces, movement, shape and momentum — describing the effects of forces between bodies; identifying different types of force; understanding vector versus scalar quantities, and that force is a vector; calculating the resultant of forces acting along a line; knowing that friction opposes motion; using force = mass × acceleration and weight = mass × gravitational field strength; understanding stopping distance as thinking distance plus braking distance and the factors affecting it; describing terminal velocity; investigating force-extension behaviour and Hooke’s law practically; describing elastic behaviour; [P] using momentum = mass × velocity, using momentum to explain safety features, using conservation of momentum, and using force = change in momentum / time taken; [P] Newton’s third law; [P] the moment of a force, the principle of moments, and beam-support problems.

Distance-time and velocity-time graphs

A distance-time graph shows how far an object has travelled over time; its gradient at any point gives the object’s speed at that instant. Average speed is calculated as:

average speed = distance moved / time taken

A velocity-time graph shows how an object’s velocity changes over time. Its gradient gives acceleration:

acceleration = change in velocity / time taken

and the area between the graph and the time axis gives the distance travelled. A third useful relationship connects final speed, initial speed, acceleration and distance directly, without needing time:

v² = u² + 2as

Worked example. A car accelerates from 5.0 m/s to 15 m/s over a distance of 40 m. Its acceleration:

v² = u² + 2as
15² = 5.0² + 2 × a × 40
225 = 25 + 80a
a = 2.5 m/s²

Forces and Newton’s second law

A force is a vector quantity that can change an object’s speed, shape or direction of motion. Where several forces act along the same line, they combine to give a single resultant force. Newton’s second law relates resultant force, mass and acceleration:

force = mass × acceleration
F = m × a

Weight is the force of gravity on a mass, related to gravitational field strength g:

weight = mass × gravitational field strength
W = m × g

Newton’s third law states that when object A exerts a force on object B, object B exerts an equal and opposite force on object A, acting on different objects along the same line. For example, when you stand on the ground, your weight pushes down on the ground, and the ground pushes up on you with an equal and opposite normal contact force — the two forces of a Newton’s third law pair always act on different objects, which is why they never cancel each other out for a single object.

Stopping distance and terminal velocity

A vehicle’s stopping distance is the sum of its thinking distance (the distance travelled while the driver reacts, affected by reaction time and speed) and its braking distance (the distance travelled while the brakes act, affected by speed, mass and road condition).

An object falling through a fluid (such as air) initially accelerates under gravity, but as its speed increases, resistive forces (such as air resistance) increase too. Eventually these balance the object’s weight, and it falls at a constant terminal velocity.

Hooke’s law and elastic behaviour

Investigating how the extension of springs, wires or rubber bands varies with applied force shows that, over an initial linear region, extension is directly proportional to the applied force — this is Hooke’s law. Elastic behaviour describes a material’s ability to return to its original shape once the deforming force is removed; beyond a certain point (the limit of proportionality), this linear, elastic behaviour no longer holds.

Momentum (Physics only)

Momentum is the product of an object’s mass and velocity:

momentum = mass × velocity
p = m × v

The conservation of momentum states that, in a closed system with no external forces, total momentum before an interaction (such as a collision) equals total momentum after it. This principle underlies vehicle safety features such as crumple zones and airbags, which extend the time over which momentum changes during a collision, reducing the force involved via:

force = change in momentum / time taken

Worked example. A 0.50 kg trolley moving at 2.0 m/s collides and sticks to a stationary 0.50 kg trolley. Using conservation of momentum, their combined velocity afterward:

(0.50 × 2.0) + (0.50 × 0) = (0.50 + 0.50) × v
1.0 = 1.0v
v = 1.0 m/s

Moments (Physics only)

The moment of a force about a pivot is the product of the force and its perpendicular distance from the pivot. The weight of a body acts through its centre of gravity. The principle of moments states that, for a system in equilibrium, the sum of clockwise moments about a pivot equals the sum of anticlockwise moments — used to analyse how the upward support forces on a beam vary with the position of a load placed along it.

Common mistakes

• Confusing gradient and area on a velocity-time graph — gradient gives acceleration, area gives distance travelled; on a distance-time graph, gradient gives speed directly.
• Forgetting that stopping distance has two separate components — thinking distance and braking distance are affected by different factors and must not be conflated.
• Assuming a stretched spring obeys Hooke’s law indefinitely — the linear relationship only holds up to the limit of proportionality.
• Mixing up momentum (mass × velocity, a vector) with kinetic energy (½mv², a scalar) — these are different quantities used in different situations.

Quick revision checklist

• average speed = distance/time; gradient and area of distance-time and velocity-time graphs
• v² = u² + 2as
• F = ma, W = mg, and resultant force along a line
• Stopping distance = thinking distance + braking distance; terminal velocity
• Hooke’s law and elastic behaviour
• p = mv, conservation of momentum, and F = Δp/Δt (Physics only)
• Moment = force × perpendicular distance, and the principle of moments (Physics only)

Related resources

• Electricity — the next topic
• Pearson Edexcel International GCSE Physics hub

Written against the Pearson Edexcel International GCSE in Physics (4PH1) specification, Issue 4. Always check the current specification for your examination year.