#### 3.1 MOTION

The key ideas used to describe and analyse the motion of objects.

Analyse the motion of objects using ICT or data-logging techniques. e.g. detecting the speed of moving vehicles, stopping distances and freefall.

#### Kinematics

You will cover:

- displacement, instantaneous speed, average speed, velocity and acceleration
- graphical representations of displacement, speed, velocity and acceleration
- Displacement-time graphs; velocity is gradient
- Velocity-time graphs – Area is distance traveled

## A Level Maths Home Study Kit

(13 Reviews) £24.99#### Linear Motion

You will cover:

- the equations of motion for constant acceleration in a straight line, including motion of bodies falling in a uniform gravitational field without air resistance

v = u + at s = ½ (u + v)t

s = ut + ½at² v² = u² + 2as - investigate the motion and collisions of objects using trolleys, air-track gliders, ticker timers, light gates, data-loggers and video techniques.
- acceleration g of free fall

how to determine the acceleration of free fall g using trapdoor and electromagnet arrangement or light gates and timer - reaction time and thinking distance; braking distance and stopping distance for a vehicle

#### Projectile Motion

You will cover:

- independence of the vertical and horizontal motion of a projectile
- motion is made of vertical and horizontal components
- two-dimensional motion of a projectile with constant velocity in one direction and constant acceleration in a perpendicular direction.

#### 3.2 FORCES IN ACTION

The motion of an object when it experiences several forces and also the equilibrium of an object. How pressure differences give rise to an upthrust on an object in a fluid.

#### Dynamics

You will cover:

- net force = mass × acceleration; F = ma
- the newton as the unit of force
- weight of an object; is a force given by W = mg
- the terms tension, normal contact force, upthrust and friction
- free-body dia-dimensional motion under constant force

#### Motion with non-uniform acceleration

You will cover:

- drag as the frictional force experienced by an object travelling through a fluid
- factors affecting drag for an object travelling through air
- motion of objects falling in a uniform gravitational field in the presence of drag
- terminal velocity
- techniques and procedures used to determine terminal velocity in fluids

ball-bearing in a viscous liquid or cones in air.

Investigating factors affecting terminal velocity.

#### Equilibrium

You will cover:

- moment of force
- couple; torque of a couple
- the principle of moments
- centre of mass; centre of gravity; experimental determination of centre of gravity
- equilibrium of an object under the action of forces and torques
- condition for equilibrium of three coplanar forces; triangle of forces.

#### Density and pressure

You will cover:

- density; ρ = mass/Volume
- pressure; p = force/Area for solids, liquids and gases
- p = hρg; upthrust on an object in a fluid;

Archimedes’ principle.

## A Level Maths Papers

(58 Reviews) £9.99#### 3.3 Work, energy and power

The link between work done and energy is explored.

Gravitational potential energy and kinetic energy are studied including the principle of conservation of energy.

#### Work and conservation of energy

You will cover:

- work done by a force; the unit joule
- W = F × d cosθ for work done by a force
- the principle of conservation of energy
- energy in different forms; transfer and conservation
- transfer of energy is equal to work done.

#### Kinetic and potential energies

You will cover:

- recall this equation and derive it from first principles

kinetic energy of an object; E_{k}= ½mv² - recall this equation and derive it from first principles

gravitational potential energy of an object in a uniform gravitational field;

E_{p}= mgh - How gravitational potential energy and kinetic energy interchange

#### Power

You will cover:

- power; the unit watt; P = W/t
- P = Fv
- efficiency of a mechanical system; efficiency = useful outpout energy/total input energy × 100%

#### 3.4 MATERIALS

This section examines the physical properties of springs and materials.

#### Springs

You will cover:

- tensile and compressive deformation; extension and compression
- Hooke’s law
- force constant k of a spring or wire; F = kx
- force-extension (or compression) graphs for springs and wires
- techniques and procedures used to investigate force-extension characteristics for arrangements which may include springs, rubber bands, polythene strips

#### Mechanical properties of matter

You will cover:

- force-extension (or compression) graph; work done is area under graph
- elastic potential energy; E = ½Fx and E = ½kx²
- stress, strain and ultimate tensile strength
- Young modulus = tensile stress/tensile strain
- techniques and procedures used to determine the Young modulus for a metal
- stress-strain graphs for typical ductile, brittle and polymeric materials
- elastic and plastic deformations of materials.

#### 3.5 Newton’s laws of motion and momentum

Fundamental laws that can predict the motion of all colliding or interacting objects. Newton’s laws can also be used to understand some of the safety features in cars, such as air bags.

#### Newton’s laws of motion

You will cover:

- Newton’s three laws of motion
- linear momentum; p = mv; vector nature of momentum
- net force = rate of change of momentum; F = Δp / Δt

F = ma is a special case of this equation. - impulse of a force; impulse = FΔt
- impulse is equal to the area under a force-time graph

#### Collisions

You will cover:

- the principle of conservation of momentum
- collisions and interaction of bodies in one dimension and in two dimensions
- perfectly elastic collision and inelastic collision

Is KE conserved?