Unit 1: Mechanics

This guide covers sub-topic 1.3 Mechanics, the first half of Unit 1: Mechanics and Materials, from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics (YPH11), Issue 3 specification (first teaching September 2018, first assessment January 2019). Unit 1 is a compulsory, externally assessed unit examined by a 1 hour 30 minute paper worth 80 marks, and this topic is commonly studied using sporting applications.

Before studying this

Unit 1 is the first unit of the International Advanced Subsidiary and International Advanced Level course and assumes GCSE/IGCSE-level physics and mathematics, including basic graph work, trigonometry (sin, cos, tan) and rearranging equations.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 1.3

Candidates will be assessed on their ability to: use the equations for uniformly accelerated motion in one dimension (v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t); draw and interpret displacement-time, velocity-time and acceleration-time graphs; know the physical quantities derived from the slopes and areas of these graphs, including cases of non-uniform acceleration, and understand how to use them; understand scalar and vector quantities, know examples of each, and recognise vector notation; resolve a vector into two components at right angles by drawing and by calculation; find the resultant of two coplanar vectors at any angle by drawing, and at right angles by calculation; understand how to make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity; draw and interpret free-body force diagrams for a particle or an extended but rigid body using the concept of centre of gravity; use ΣF = ma, understanding its use where m is constant (Newton’s second law), including Newton’s first law where a = 0 (objects at rest or at constant velocity, with the term “terminal velocity” expected); use g = F/m and W = mg; CORE PRACTICAL 1: determine the acceleration of a freely-falling object; know and understand Newton’s third law and the properties of pairs of forces in an interaction between two bodies; understand that momentum is defined as p = mv; know the principle of conservation of linear momentum, understand how to relate this to Newton’s laws, and apply it to one-dimensional problems; use the equation for the moment of a force, moment = Fx, where x is the perpendicular distance between the line of action of the force and the axis of rotation; use the concept of centre of gravity and apply the principle of moments to an extended body in equilibrium; use the equation for work, ΔW = FΔs, including calculations when the force is not along the line of motion; use Ek = ½mv² for kinetic energy; use ΔEgrav = mgΔh for the change in gravitational potential energy near the Earth’s surface; know and apply the principle of conservation of energy, including work done, gravitational potential energy and kinetic energy; use the equations relating power, time and energy transferred or work done, P = E/t and P = W/t; and use the equations for efficiency, efficiency = useful energy output / total energy input and efficiency = useful power output / total power input.

Uniformly accelerated motion

For an object moving in a straight line with constant acceleration a, starting at velocity u and reaching velocity v after time t, having travelled displacement s, the four equations of motion (the “SUVAT” equations) are:

v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t

These equations only apply while acceleration is constant. On a displacement-time graph, the gradient at any point gives velocity; on a velocity-time graph, the gradient gives acceleration and the area under the graph gives displacement, including for cases of non-uniform acceleration where the graph is curved and the area must be estimated (for example by counting squares or using calculus-style graphical methods).

Vectors and projectile motion

A scalar quantity has magnitude only (e.g. speed, distance, energy); a vector quantity has magnitude and direction (e.g. velocity, displacement, force), and is written in bold or with an arrow above the symbol. A vector can be resolved into two components at right angles, typically horizontal and vertical, using cos θ and sin θ. Two coplanar vectors can be combined into a single resultant vector by scale drawing (any angle) or by calculation (right angles, using Pythagoras’ theorem and trigonometry).

Projectile motion — an object moving freely under gravity with an initial horizontal velocity — is analysed by treating the horizontal and vertical components of motion as independent: horizontal velocity stays constant (no horizontal force, ignoring air resistance), while the vertical motion accelerates at g = 9.81 m/s² under gravity, governed by the SUVAT equations.

Newton’s laws, momentum and moments

Newton’s first law: an object remains at rest or at constant velocity unless acted on by a resultant force (a = 0). Newton’s second law: ΣF = ma for constant mass — the resultant force on an object equals its mass multiplied by its acceleration. When resultant force is zero, an object falling through a fluid reaches terminal velocity. Newton’s third law: for every action force there is an equal and opposite reaction force, and the two forces act on different bodies, are of the same type, and act along the same line.

Weight is the force of gravity on a mass: W = mg, where g = F/m is the gravitational field strength. CORE PRACTICAL 1 determines the acceleration of a freely-falling object, typically using light gates or strobe/video photography.

Momentum is defined as p = mv. The principle of conservation of linear momentum states that, in a closed system with no external resultant force, total momentum before an interaction equals total momentum after — this follows from Newton’s third law applied to the equal and opposite forces (and equal and opposite impulses) the two bodies exert on each other during a collision.

The moment of a force about a point is moment = Fx, where x is the perpendicular distance from the line of action of the force to the axis of rotation. An extended body’s weight can be treated as acting through its centre of gravity, and the principle of moments — for a body in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments — is used to solve beam-support and balance problems.

Work, energy and power

Work done is ΔW = FΔs; when the force is not along the line of motion, only the component of force along the direction of displacement does work. Kinetic energy is Ek = ½mv², and the change in gravitational potential energy near the Earth’s surface is ΔEgrav = mgΔh. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between stores — used together with work done, gravitational potential energy and kinetic energy to solve problems such as objects sliding down slopes or projectiles rising and falling.

Power is the rate of energy transfer or of doing work: P = E/t and P = W/t. Efficiency compares useful output to total input:

efficiency = useful energy output / total energy input
efficiency = useful power output / total power input

Worked example. A ball of mass 0.20 kg is thrown horizontally from a cliff at 12 m/s and lands 1.5 s later. Find (a) the horizontal distance travelled, and (b) the vertical velocity on landing (take g = 9.81 m/s² and ignore air resistance).

(a) Horizontal motion is at constant velocity (no horizontal force): horizontal distance = 12 × 1.5 = 18 m.

(b) Vertical motion starts from rest (u = 0 vertically) and accelerates at g: v = u + at = 0 + (9.81 × 1.5) = 14.7 m/s (downward). The horizontal and vertical components are treated entirely independently.

Common mistakes

Forgetting that the SUVAT equations only hold for constant acceleration, and misapplying them to curved velocity-time graphs where acceleration varies. Confusing mass (a scalar, in kg) with weight (a vector force, in N). Treating projectile motion’s horizontal and vertical components as linked rather than independent — for example, assuming a heavier projectile falls “faster” horizontally. Applying Newton’s third-law pair to the same body instead of two different interacting bodies. Forgetting that the perpendicular distance, not the direct distance, must be used when calculating a moment.

Quick revision checklist

• State and use all four SUVAT equations for uniformly accelerated motion.
• Interpret displacement-time, velocity-time and acceleration-time graphs, including non-uniform acceleration.
• Resolve and combine vectors by drawing and by calculation.
• Analyse projectile motion using independent horizontal and vertical components.
• State Newton’s first, second and third laws and apply ΣF = ma.
• Use g = F/m, W = mg, and describe CORE PRACTICAL 1 (acceleration of a freely-falling object).
• Define momentum p = mv and apply conservation of linear momentum.
• Calculate moments (moment = Fx) and apply the principle of moments to an extended body.
• Use ΔW = FΔs, Ek = ½mv², ΔEgrav = mgΔh, and the conservation of energy principle.
• Use P = E/t, P = W/t, and calculate efficiency from energy or power ratios.

Related resources

• Unit 1: Materials — the next sub-topic, completing Unit 1
• Unit 2: Waves and Particle Nature of Light — the next unit
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.