Motion: Speed, Velocity and Acceleration

• Speed is the distance travelled per unit time
• Acceleration or deceleration occurs when speed is changing
• Free fall acceleration near Earth is constant
• Average speed = total distance / total time
• Velocity is the speed in a specific direction
• Acceleration is the change in velocity per unit time
• Acceleration = change in velocity / time taken
• a = (v-u)/t
• (final speed)² = (initial speed)² + (2 × acceleration × distance)
• v² = u² + 2as
• Distance is measured in metres (m), time in seconds (s), speed and velocity in metres per second (m/s), and acceleration in metres per second squared (m/s²)

Displacement-Time Graphs

• The gradient is velocity
• A negative gradient means returning to the starting point
• A horizontal line indicates the object is stationary
• Zero displacement means returning to the starting point
• A curved line indicates changing velocity, thus acceleration or deceleration

Velocity-Time Graphs

• The gradient is acceleration
• A negative gradient means negative acceleration, also known as deceleration
• Zero speed indicates the object is at rest
• A horizontal line represents constant speed
• The area under the line is the distance travelled
• A curved line means acceleration is changing

Vectors and Scalars

• A vector has magnitude and direction
• A scalar has just a magnitude

Examples

• Scalars: Distance, Speed, Time, Energy
• Vectors: Displacement, Velocity, Acceleration, Force

Effects of Forces

• Forces can change the speed, shape or direction of a body
• Forces are measured in Newtons (N)
• Examples of forces: gravitational, electrostatic
• Friction is a force between two surfaces which impedes motion and results in heating, air resistance is a form of friction
• Resultant forces acting along the same line should be added together if in the same direction and subtracted if in the opposite direction

Newton's Laws of Motion

• First law: An object maintains constant velocity unless acted on by a resultant force
• Second law: force = mass × acceleration (F = ma)
• Third law: Every action force has an equal and opposite reaction force; the force of the Earth's gravity on an object is equal and opposite to the force of the object's gravity on the Earth

Mass and Weight

• Mass is a measure of how much matter is in an object, measured in kilograms (kg)
• Weight is a gravitational force (the effect of a gravitational field on a mass)
• weight = mass × gravitational field strength
• W = mg
• Gravitational field strength on Earth is 10N/kg
• The weight of an object acts through its centre of gravity

Motion of a Body Falling in a Uniform Gravitational Field:

• Initially, there is no air resistance, only weight acts on the body
• As the body falls, it accelerates, increasing its speed and air resistance
• The resultant force downwards decreases
• The acceleration decreases, slowing the rate of speeding up
• Eventually, air resistance and weight are equal and opposite, resulting in no resultant force
• No acceleration occurs and terminal velocity is reached

Driver Hazards

• Thinking distance is the distance travelled between realizing the need to brake and pressing the brakes
• Factors increasing thinking distance: greater speed and slower reaction time due to alcohol, tiredness, or distractions
• Reaction time can be reduced by caffeine
• Braking distance is the distance travelled between pressing the brakes and the vehicle stopping
• Factors increasing braking distance: greater speed or mass, poor road conditions (icy, wet), or car conditions (worn tires, worn brake pads)
• Stopping distance is the sum of thinking distance and braking distance.

Deformation

• A force may produce a change in size and shape of a body
• Elastic deformation occurs when an object returns to its original shape after the load is removed
• An example is a spring being stretched under normal usage

Hooke's Law

• Hooke's law states that for a spring, F = kx where F is the force applied to the spring, k is the spring constant, and x is the extension

Force-Extension Graphs

• Linear (straight line) graphs represent elastic deformation following Hooke's law
• The limit of proportionality is the point where the graph stops being linear and Hooke's law no longer applies
• Gradient is the spring constant, k
• Non-linear (curved line) graphs represent deformation that does not follow Hooke's law
• After this region, the material will fracture

Moments

• Moment of a force is a measure of its turning effect, measured in Newton metres (Nm)
• moment = force × perpendicular distance from the pivot
• moment = Fd
• Equilibrium occurs when the sum of clockwise moments equals the sum of anticlockwise moments (the principle of moments) and there is no resultant force
• For a horizontal beam supported at its ends, the upwards forces at the supports change with the position of a heavy object placed on the beam. The nearer the heavy object to a given support, the greater the force at that support.

Momentum

• Momentum of an object is the product of its mass and velocity
• momentum = mass × velocity
• p = mv
• Measured in kilogram metres per second (kgm/s)
• Force exerted on an object equals its change in momentum over time
• force = change in momentum/ time taken
• F = (mv-mu) / t
• Car safety features increase the time taken for people in the car to come to rest (i.e. there is the same change in momentum in a longer time, so the force is reduced), for example, a seatbelt achieves this by stretching
• In a collision, the total momentum before the collision is equal to the total momentum afterwards
• Known as the principle of the conservation of momentum