MotionCopy

Cheat Sheet: Motion (O Level / IGCSE Physics)

1. Definitions

• Speed = distance travelled ÷ time taken
  → Speed = s / t
  (Scalar quantity)
• Velocity = change in displacement ÷ time taken
  → Velocity = ∆s / t
  (Vector quantity)

2. Key Equations

• Speed:
  v = s / t
• Average Speed:
  average speed = total distance / total time
• Acceleration:
  a = ∆v / ∆t
  = (final velocity − initial velocity) / time

3. Acceleration Types

• Uniform Acceleration:
  Constant change in velocity (e.g., freely falling object)
• Non-uniform Acceleration:
  Changing rate of acceleration (e.g., car braking erratically)
• Deceleration:
  Negative acceleration (velocity decreases)

4. Graph Interpretation

Distance–Time Graph

• At rest: horizontal line (zero gradient)
• Constant speed: straight, sloped line
• Acceleration: curve with increasing gradient
• Deceleration: curve with decreasing gradient

Speed–Time Graph

• At rest: horizontal line on x-axis (speed = 0)
• Constant speed: horizontal line above x-axis
• Constant acceleration: straight upward slope
• Changing acceleration: curve (non-linear slope)

5. Free Fall

• Near Earth’s surface:
  Acceleration due to gravity, g ≈ 9.8 m/s²
• Applies to all objects regardless of mass (ignoring air resistance)

6. From Graphs

Gradient of Distance–Time Graph

• Gradient = speed
  (steeper = faster)

Area Under Speed–Time Graph

• Distance travelled = area under graph
  • For constant speed: area = rectangle = base × height
  • For constant acceleration: area = triangle = ½ × base × height
  • For varying speed: divide into sections (rectangles + triangles)

Gradient of Speed–Time Graph

• Gradient = acceleration
  • Positive gradient = acceleration
  • Negative gradient = deceleration
  • Steeper gradient = greater acceleration