2.2 Motion
Measuring How Far You've Gone
There are two ways to describe "how far" — and they give different answers.
There are two ways to describe "how far" — and they give different answers.
⚡ Key Definitions:
• Distance (scalar): The total length of the path travelled
• Displacement (vector): The straight-line distance and direction from start to finish
• Displacement (vector): The straight-line distance and direction from start to finish
Distance
Total Path
Scalar (no direction)
Always positive
"How far did you walk?"
Displacement
Start → Finish
Vector (has direction)
Can be zero
"How far are you from start?"
Example: Running Around a Track
You run one complete lap of a 400 m running track, ending exactly where you started.
Distance travelled: 400 m (total path)
Displacement: 0 m (you're back at start.)
This is why distance and displacement are different.
Displacement: 0 m (you're back at start.)
This is why distance and displacement are different.
Example: Walking to School
You walk 300 m East, then 400 m North to reach school.
Distance: 300 + 400 = 700 m
Displacement: Straight line from start to school
Using Pythagoras: $\sqrt{300^2 + 400^2} = \sqrt{250000} = $ 500 m (North-East direction)
Distance: 300 + 400 = 700 m
Displacement: Straight line from start to school
Using Pythagoras: $\sqrt{300^2 + 400^2} = \sqrt{250000} = $ 500 m (North-East direction)
🎯 Distance or Displacement Practice
Measuring How Fast You're Going
Just like distance and displacement, there are two ways to describe "how fast".
Just like distance and displacement, there are two ways to describe "how fast".
⚡ Key Definitions:
• Speed (scalar): How fast you're going — rate of change of distance
• Velocity (vector): Speed in a given direction — rate of change of displacement
• Velocity (vector): Speed in a given direction — rate of change of displacement
Speed/Velocity Equation:
v = d / t
v = speed (m/s) | d = distance (m) | t = time (s)
Example 1: Calculating Speed
A car travels 150 m in 10 seconds. What is its speed?
Step 1: Write the formula
v = d / t
Step 2: Substitute values
v = 150 / 10
Step 3: Calculate
v = 15 m/s
Step 1: Write the formula
v = d / t
Step 2: Substitute values
v = 150 / 10
Step 3: Calculate
v = 15 m/s
Example 2: Finding Distance
A cyclist travels at 8 m/s for 25 seconds. How far do they travel?
Rearrange: d = v × t
d = 8 × 25
d = 200 m
Rearrange: d = v × t
d = 8 × 25
d = 200 m
Example 3: Finding Time
A runner covers 400 m at an average speed of 5 m/s. How long does it take?
Rearrange: t = d / v
t = 400 / 5
t = 80 s
Rearrange: t = d / v
t = 400 / 5
t = 80 s
🎯 Speed Calculation Practice
Measuring How Quickly Velocity Changes
Acceleration is the rate at which an object's velocity changes. It is a vector quantity measured in m/s².
Acceleration is the rate at which an object's velocity changes. It is a vector quantity measured in m/s².
⚡ When is Something Accelerating?
An object is accelerating if it is:
• Speeding up (positive acceleration)
• Slowing down (negative acceleration / deceleration)
• Changing direction (even at constant speed)
• Speeding up (positive acceleration)
• Slowing down (negative acceleration / deceleration)
• Changing direction (even at constant speed)
Speeding Up
+ve acceleration
Slowing Down
−ve acceleration
Changing Direction
Also accelerating
Acceleration Equation:
a = (v − u) / t
a = acceleration (m/s²) | v = final velocity (m/s) | u = initial velocity (m/s) | t = time (s)
Example 1: Calculating Acceleration
A car speeds up from 10 m/s to 30 m/s in 5 seconds. What is its acceleration?
Step 1: Identify values
u = 10 m/s, v = 30 m/s, t = 5 s
Step 2: Apply formula
a = (v − u) / t
a = (30 − 10) / 5
a = 20 / 5
a = 4 m/s²
Step 1: Identify values
u = 10 m/s, v = 30 m/s, t = 5 s
Step 2: Apply formula
a = (v − u) / t
a = (30 − 10) / 5
a = 20 / 5
a = 4 m/s²
Example 2: Deceleration (Negative Acceleration)
A bike slows from 15 m/s to 5 m/s in 4 seconds. What is its acceleration?
a = (v − u) / t
a = (5 − 15) / 4
a = −10 / 4
a = −2.5 m/s²
The negative sign shows deceleration (slowing down).
a = (v − u) / t
a = (5 − 15) / 4
a = −10 / 4
a = −2.5 m/s²
The negative sign shows deceleration (slowing down).
🎯 Acceleration Practice
m/s²
m/s²
Reading Distance-Time Graphs
A distance-time graph shows how the distance travelled changes over time.
A distance-time graph shows how the distance travelled changes over time.
⚡ Key Rules for D-T Graphs:
• Flat line: Object is stationary (not moving)
• Straight sloped line: Constant speed
• Steeper line: Faster speed
• Curved line: Acceleration (changing speed)
• Gradient = Speed
• Straight sloped line: Constant speed
• Steeper line: Faster speed
• Curved line: Acceleration (changing speed)
• Gradient = Speed
Distance-Time Graph Examples
A: Stationary
B: Constant speed
C: Faster constant speed
D: Accelerating
📊 Gradient = Speed
Speed = rise ÷ run = Δdistance ÷ Δtime
📏 Steeper = Faster
A steeper line means higher speed
➡️ Flat = Stopped
Horizontal line means not moving
🔄 Curve = Accelerating
Curved line means speed is changing
🎯 D-T Graph Interpretation
Reading Velocity-Time Graphs
A velocity-time graph shows how velocity changes over time. These graphs give us even more information than D-T graphs.
• Positive slope = speeding up
• Negative slope = slowing down
• Zero slope = constant velocity
• Rectangle: base × height
• Triangle: ½ × base × height
• Combine shapes if needed
A velocity-time graph shows how velocity changes over time. These graphs give us even more information than D-T graphs.
⚡ Key Rules for V-T Graphs:
• Flat line at zero: Object is stationary
• Flat line (not zero): Constant velocity
• Sloped line: Constant acceleration
• Gradient = Acceleration
• Area under graph = Distance travelled
• Flat line (not zero): Constant velocity
• Sloped line: Constant acceleration
• Gradient = Acceleration
• Area under graph = Distance travelled
Velocity-Time Graph Examples
A: Constant velocity
B: Accelerating
C: Decelerating
D: Stationary
Gradient = Acceleration
a = Δv / Δt• Positive slope = speeding up
• Negative slope = slowing down
• Zero slope = constant velocity
Area = Distance
Area under the graph = distance travelled• Rectangle: base × height
• Triangle: ½ × base × height
• Combine shapes if needed
Example: Finding Distance from V-T Graph
A car travels at 20 m/s for 10 seconds (constant velocity).
Area under graph: Rectangle
Area = base × height
Area = 10 × 20
Distance = 200 m
Area under graph: Rectangle
Area = base × height
Area = 10 × 20
Distance = 200 m
Example: Finding Acceleration from V-T Graph
Velocity increases from 0 to 30 m/s in 6 seconds.
Gradient = Acceleration:
a = (v − u) / t
a = (30 − 0) / 6
a = 5 m/s²
Gradient = Acceleration:
a = (v − u) / t
a = (30 − 0) / 6
a = 5 m/s²
🎯 V-T Graph Interpretation
Real Life Uses:
• GPS Navigation: Calculates speed from distance and time
• Speed Cameras: Measure average speed between two points
• Athletics: Timing races and calculating average speeds
• Car Dashboards: Speedometers show instantaneous speed
• Physics Experiments: Light gates measure velocity precisely
• GPS Navigation: Calculates speed from distance and time
• Speed Cameras: Measure average speed between two points
• Athletics: Timing races and calculating average speeds
• Car Dashboards: Speedometers show instantaneous speed
• Physics Experiments: Light gates measure velocity precisely