The difference between average speed and instantaneous speed lies in how they are measured over time:

1. Average Speed: This is the total distance traveled divided by the total time taken. It represents the overall speed for the entire duration of a trip or motion. Mathematically, it’s expressed as:

   $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

   It gives an overall measure but doesn't reflect variations in speed at any given moment during the journey.

2. Instantaneous Speed: This is the speed of an object at a particular instant of time. It is the speed measured at a specific point rather than over a period of time. It can be found by taking the derivative of distance with respect to time when considering calculus.

   $v_{\text{instantaneous}} = \lim_{\Delta t \to 0} \frac{\Delta d}{\Delta t}$

   Instantaneous speed can vary throughout a journey, while average speed smooths out these variations.

Which did we measure in this activity?

• If you measured the time taken to travel a specific distance and then calculated speed using total distance and time, you measured average speed.
• If you recorded the speed at a specific moment in time, such as reading the speed from a speedometer, you measured instantaneous speed.

Would you like more details or have any questions?

5 Related Questions:

1. How can we measure instantaneous speed practically in real life?
2. What factors can cause variations in instantaneous speed?
3. Can average speed ever equal instantaneous speed? Under what conditions?
4. How does velocity differ from both average and instantaneous speed?
5. What role does acceleration play in changes to instantaneous speed?

Tip: Instantaneous speed can be obtained from the slope of a distance-time graph at a specific point!