Average Speed

Definition

In kinematics and calculus, average speed measures the overall rate at which distance is covered over a specific time interval.

Why It Matters

Average speed provides the macro view of a journey. It allows us to estimate total travel time and understand overall efficiency, even if the actual speed fluctuates wildly throughout the trip.

Core Concepts

• Average Speed Formula: The average speed of an object over a time interval $[t_1, t_2]$ is the total distance traveled divided by the elapsed time: $\text{Average speed} = \frac{\Delta y}{\Delta t} = \frac{f(t_2) - f(t_1)}{t_2 - t_1}$
  • How to read: “The average speed is the change in y divided by the change in t, which is the ratio of the difference f of t two minus f of t one to the difference t two minus t one.”
  • Meaning: Total displacement (or distance, if always moving forward) divided by elapsed time—this corresponds to the slope of a secant line on a position-time graph.

Connected Concepts

• Instantaneous Speed
• Average Rate of Change and Secant Lines
• Area by Double Integration
• Average Value by Double Integration