Acceleration and Velocity Time Graphs

Key Concepts

• Acceleration: Change in velocity over a given time. Calculated using: [ \text{Acceleration (m/s}^2\text{)} = \frac{\text{Change in Velocity (m/s)}}{\text{Time (s)}} ]
• Velocity: Speed in a given direction; a vector quantity with both magnitude and direction.

Calculating Acceleration

1. Equation:
   • Not provided in exams; must be memorized.
   • Acceleration = (Final Velocity - Initial Velocity) / Time

Example 1: Car Acceleration

• Given: Initial velocity = 15 m/s north, Final velocity = 35 m/s north, Time = 20 s
• Calculation:
  • Change in velocity = 35 - 15 = 20 m/s
  • Acceleration = 20 m/s / 20 s = 1 m/s²
• Interpretation: Car increases velocity by 1 m/s every second for 20 seconds.

Example 2: Cyclist Deceleration

• Given: Initial velocity = 6 m/s east, Final velocity = 0 m/s, Time = 12 s
• Calculation:
  • Change in velocity = 0 - 6 = -6 m/s
  • Acceleration = -6 m/s / 12 s = -0.5 m/s²
• Interpretation: Negative acceleration indicates deceleration.

Velocity Time Graphs

• Gradient: Indicates acceleration.
  • Horizontal line: Constant velocity.
  • Upward slope: Acceleration.
  • Downward slope: Deceleration.

Example: Acceleration and Deceleration

• First Part:
  • Final velocity = 15 m/s, Initial velocity = 0 m/s, Time = 100 s
  • Acceleration = (15 m/s - 0 m/s) / 100 s = 0.15 m/s²
• Last Part:
  • Final velocity = 0 m/s, Initial velocity = 15 m/s, Time = 300 s
  • Acceleration = (0 m/s - 15 m/s) / 300 s = -0.05 m/s²

Calculating Displacement from Velocity Time Graph

• Total Area Under Graph: Equals distance travelled (displacement).
• Constant Acceleration/Deceleration: Divide graph into shapes and calculate area.
  • Example Areas: Triangle = 750, Rectangle = 1500, Triangle = 2250
  • Total Displacement = 750 + 1500 + 2250 = 4500 meters

Non-Constant Acceleration/Deceleration

• Count Squares:
  • Complete squares = 15, Partial squares = 5
  • Total = 20 squares
  • Each square area = 250
  • Total Displacement = 20 * 250 = 5000 meters*

Study Resources

• Practice questions on acceleration and velocity time graphs available in revision workbook.