Describing motion

Kinematics

The study of motion without considering the forces that cause it

Importance of Kinematics in Road Safety

Used to understand speed limits

Importance of Kinematics in Sports

Athletes and coaches analyze distance-time and speed-time graphs to measure performance and track improvement

Importance of Kinematics in Space & Aviation

Velocity and acceleration are vital for controlling the take-off

Importance of Kinematics in Theme Parks

Roller coaster designers use speed-time graphs to predict safe acceleration and deceleration

Importance of Kinematics in GPS & Mobile Apps

Apps like Google Maps and Uber calculate average speed to estimate arrival times

Importance of Kinematics in Medicine

Doctors use graphs of heartbeat and breathing rates to detect abnormalities

Importance of Kinematics in Engineering & Construction

Machines like cranes

Speed

A measure of how fast an object is moving

calculated as distance divided by time

Distance

The total path traveled by an object

Time

The duration of motion

Formula for Speed

Speed = Distance ÷ Time

Average Speed

Total distance traveled divided by total time taken

Average Speed Formula

Average Speed = Total Distance ÷ Total Time

Example of Average Speed

A car travels 100 m in 10 s → Average speed = 100 ÷ 10 = 10 m/s

Practical Determination of Speed (Two Light Gates)

A peg passes through two light gates

timer starts at the first and stops at the second

speed = distance between gates ÷ time taken

Practical Determination of Speed (One Light Gate + Interrupt Card)

A card on a trolley breaks and clears a light beam

speed = length of card ÷ time beam was blocked

Scalar Quantity

Has only magnitude (size)

examples: speed

mass

Vector Quantity

Has both magnitude and direction

examples: velocity

displacement

Difference Between Speed and Velocity

Velocity is speed in a given direction

velocity is vector (includes direction)

Distance-Time Graph

A graph showing distance traveled against time

used to describe motion

Flat Line on Distance-Time Graph

Object is stationary (speed = 0)

Straight Sloping Line on Distance-Time Graph

Object moving at a constant speed

Increasing Slope on Distance-Time Graph

Object is accelerating (speed increasing)

Decreasing Slope on Distance-Time Graph

Object is decelerating (speed decreasing)

Gradient of a Distance-Time Graph

Represents the speed of the object

gradient = change in distance ÷ change in time

Acceleration

The rate of change of speed or velocity over time

Formula for Acceleration

Acceleration = Change in Speed ÷ Time Taken (a = Δv ÷ Δt)

Unit of Acceleration

Meters per second squared (m/s²)

Example of Acceleration

A car accelerates from 0 to 20 m/s in 5 s → a = (20 − 0) ÷ 5 = 4 m/s²

Deceleration

Negative acceleration

the object slows down

Speed vs Velocity

Speed = scalar (magnitude only)

Velocity = vector (magnitude and direction)

Scalars Examples

Speed

Vectors Examples

Velocity

Speed-Time Graph

A graph showing speed against time

used to analyze acceleration and distance

Flat Line on Speed-Time Graph

Object moving at a constant speed

Upward Sloping Line on Speed-Time Graph

Speed is increasing (acceleration)

Downward Sloping Line on Speed-Time Graph

Speed is decreasing (deceleration)

Line on X-axis (Speed = 0)

Object is stationary

Gradient of a Speed-Time Graph

Represents acceleration

acceleration = change in speed ÷ time taken

Meaning of Negative Gradient

Indicates deceleration (speed decreasing)

Area Under a Speed-Time Graph

Represents the distance traveled

Area of Rectangle

Width × Height

Area of Triangle

½ × Base × Height

Curved Speed-Time Graph

Indicates changing acceleration (non-uniform)

Straight Sloping Line on Speed-Time Graph

Constant acceleration (uniform rate of change)

Downward Sloping Straight Line

Constant deceleration (uniform slowing down)

Relationship Between Gradient and Acceleration

Steeper gradient = greater acceleration

Relationship Between Area and Distance

Larger area under the graph = greater distance traveled

Acceleration in Straight Line Motion

The object must be moving in a straight line for acceleration to apply directly from the graph

Changing Acceleration

If the speed-time graph is curved

Units Recap

Distance → meters (m)

Time → seconds (s)

Speed → m/s

Acceleration → m/s²

Summary of Key Formulas

Speed = Distance ÷ Time

Average Speed = Total Distance ÷ Total Time

Acceleration = (Final Speed − Initial Speed) ÷ Time

Gradient = Acceleration

Area = Distance