29. Velocity-Time Graphs

1. Core Principles

• Function: Velocity-time graphs show how an object's velocity (speed in a direction) changes over time.

• The Gradient: The gradient of the line represents the acceleration.

• Gradient = Change in Velocity / Change in Time = Acceleration

• Area Under the Curve: The total area under the graph represents the distance traveled.

• Area Under the Curve: The total area under the graph represents the distance traveled.

2. Interpreting the Shapes

• Straight Diagonal Line (Upwards): Represents constant acceleration.

• Straight Diagonal Line (Downwards): Represents constant deceleration.

• Horizontal (Flat) Line: Represents constant velocity (acceleration is zero).

• Steepening Curve: Indicates that the rate of acceleration is increasing.

3. Calculating Acceleration and Distance

Calculating Acceleration

• Pick a straight section of the graph and divide the change in velocity by the change in time.

• Example: If velocity increases by 3 m/s over 2 seconds, the acceleration is 3 / 2 = 1.5 m/s²

Calculating Distance (Area Under the Graph)

• For Straight Sections: Split the area under the line into simple shapes like triangles and rectangles.

  • Triangle Area: ½ base x height

  • Rectangle Area: base x height

  • Add these areas together to get the total distance in meters (m).

• For Curved Sections: You can estimate the area by counting the squares on the grid.

  • Combine partially full squares to estimate full ones.

  • Multiply the number of squares by the "value" of one square (e.g., if one square represents 1 m, then 8 squares = 8 m).

4. Summary Table