Motion Quantities: Distance, Displacement, Speed, and Velocity

Learning Intentions (LISC):
- To understand that the motion of objects can be described and predicted according to ACSSU229.
- To explain qualitatively the relationship between distance and displacement.
- To explain the fundamental differences between speed and velocity.
- To describe the relationships between variables such as displacement, time, and the equations of motion.
Success Criteria:
- Ability to state standard units for speed, distance, time, and acceleration.
- Ability to define and apply the terms speed, distance, time, and velocity in various contexts.

Scalar Quantities:
- A scalar quantity is defined as a measurement that consists of only a magnitude (a numerical value) accompanied by units.
- Examples of scalar quantities include:
  - Distance
  - Speed
Vector Quantities:
- While the transcript notes are cut off regarding vectors, in the context of motion, vectors are quantities that possess both a magnitude (with units) and a specific direction.
- Examples of vector quantities mentioned in subsequent sections include displacement and velocity.

Distance ( $d$ ):
- Distance is a measure of how far an object travels during its motion.
- It is a scalar quantity.
- The standard unit of measurement for distance is the metre ( $m$ ).
Displacement ( $r$ or $s$ ):
- Displacement is a measure of the straight-line distance between the starting point and the finishing point (the "as the crow flies" distance).
- Because it is a vector quantity, it is mandatory to provide a direction along with the magnitude.
- The standard unit of measurement for displacement is also the metre ( $m$ ).
Activity Scenarios:
- Scenario A to B (Page 5): Involves calculating distance based on segments measuring $10\,m$ , $10\,m$ , and $5\,m$ .
- Scenario A to B (Page 6): Involves calculating distance based on segments measuring $2\,m$ , $3\,m$ , $3\,m$ , and $2\,m$ .

Speed ( $v$ ):
- Speed is defined as the rate of change of distance.
- It describes how fast or slow an object is moving.
- It is a scalar quantity.
- Standard units: Metres per second ( $m/s$ or $ms^{-1}$ ).
- Symbol variation: While $v$ is common, speed is also sometimes represented by the symbol $s$ .
Velocity ( $v$ ):
- Velocity is defined as the rate of change of displacement.
- Unlike speed, velocity is a vector quantity and must include a direction.
- Standard units: Metres per second ( $m/s$ or $ms^{-1}$ ).

Calculating Speed:
- The formula for speed is represented as: $v = \frac{d}{t}$
- Where:
  - $v = \text{speed (measured in } m/s \text{ or } ms^{-1})$
  - $d = \text{distance (measured in } m)$
  - $t = \text{time (measured in } s)$
Calculating Velocity:
- The formula for velocity is represented as: $v = \frac{s}{t}$
- Where:
  - $v = \text{velocity (measured in } m/s \text{ or } ms^{-1})$
  - $s = \text{displacement (measured in } m)$
  - $t = \text{time (measured in } s)$
Example Calculation (Travelling 3m East for 40 seconds):
- Speed Calculation: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ $\text{Speed} = \frac{3\,m}{40\,s}$ $\text{Speed} = 0.075\,m/s$

Instantaneous Speed or Velocity:
- This refers to the speed or velocity of an object at a specific, single moment in time.
- Real-world Application: In a vehicle, this is measured by the speedometer. It is also the value captured by a speed camera.
Average Speed or Velocity:
- This provides a measurement of the motion over the course of the entire journey.
- It looks at the journey as a whole and ignores any specific stops, starts, or variations in speed that occurred during the trip.