. If f(t) is the position of a moving object at time t, what does the average rate of change of f on an interval [t1, t2] represent? (i) Average time of travel (ii) Average distance traveled (iii) Average velocity

If \( f(t) \) represents the position of a moving object at time \( t \), then the average rate of change of \( f(t) \) on the interval \([t_1, t_2]\) is given by:

\[
\text{Average Rate of Change} = \frac{f(t_2) - f(t_1)}{t_2 - t_1}
\]

This formula represents the **average velocity** of the object over the time interval \([t_1, t_2]\). The average velocity is the total change in position (i.e., displacement) divided by the total time elapsed.

Thus, the correct answer is:

**(iii) Average velocity**

Would you like any further details or have any questions?

Here are 5 related questions:

1. How do you interpret the average velocity if the object changes direction during the interval?
2. What is the difference between average velocity and instantaneous velocity?
3. How can the average velocity be zero even if the object has moved?
4. How does the average velocity relate to the concept of speed?
5. What would the average rate of change represent if \( f(t) \) were the temperature at time \( t \) instead of position?

**Tip:** Average velocity considers only the net change in position, not the actual path traveled.

Explore the concept of average rate of change in calculus through a detailed explanation of its formula and application. Learn how it relates to velocity when considering the position of a moving object over a specified interval. Suitable for high school students and above.

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