2.2 Motion
Distance vs. Displacement
Distance is a scalar quantity. It measures the total amount of distance you have travelled.
Displacement is a vector quantity. It measures the straight-line distance and direction from your starting point to your ending point.
Example: If you run one lap of a 400 m running track and end up exactly where you started:
- Your distance travelled is 400 m.
- Your displacement is 0 m (because you are back at your start).
Speed vs. Velocity
Speed is the scalar quantity that measures how fast you are going (the rate of change of distance).
Velocity is the vector quantity that measures the rate of change of displacement. It is speed in a given direction.
Average speed is calculated using the equation: Average Speed = Distance Travelled / Time Taken
v = d / t
Where:
- v is speed in metres per second (m/s)
- d is distance in metres (m)
- t is time in seconds (s)
Acceleration is the rate at which an object's velocity changes. It is a vector quantity, measured in metres per second squared (m/s²).
An object is accelerating if it is:
- Speeding up
- Slowing down (this is also called deceleration)
- Changing direction (even if its speed is constant!)
We can calculate acceleration using the equation:
Acceleration = (Final Velocity - Initial Velocity) / Time
Taken
a = (v - u) / t
Where:
- a is acceleration in metres per second squared (m/s²)
- v is the final velocity in metres per second (m/s)
- u is the initial velocity in metres per second (m/s)
- t is the time taken in seconds (s)
If the acceleration is negative, it means the object is slowing down (decelerating).
We can represent an object's journey using two main types of graphs.
Distance-Time Graphs
- A flat line means the object is stationary (not moving).
- A straight, sloped line means the object is moving at a constant speed.
- The steeper the line, the faster the speed.
- A curved line means the object is accelerating (speeding up or slowing down).
Velocity-Time Graphs
- A flat line at zero means the object is stationary.
- A flat line (not at zero) means the object is moving at a constant velocity.
- A straight, sloped line means the object is moving with constant acceleration.
- The gradient (steepness) of the line tells you the acceleration.
- The area under the graph tells you the distance travelled.