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For the given problem:

### Part a:
- \( s(5) - s(2) \) = 184.05 miles. 
- This represents the total distance traveled by the truck from \( t = 2 \) hours to \( t = 5 \) hours.

### Part b:
- The average velocity over the interval \( t_1 = 2 \) to \( t_2 = 5 \) is approximately 61.35 miles per hour.

Would you like more detailed steps or have any further questions?

Here are some related questions to explore:
1. What is the physical significance of the derivative of \( s(t) \)?
2. How can we compute the instantaneous velocity at \( t = 3 \)?
3. How would the result change if the function \( s(t) \) were different?
4. How do we interpret average velocity when \( s(t) \) is non-linear?
5. What would be the result if we calculated \( s(7) - s(3) \)?

**Tip:** The average velocity over an interval is the slope of the secant line between the two points on the distance-time graph.

Average velocity. Suppose that in t hours, a truck travels s(t) miles, where s(t) = 40t^1.2. a) Find s(5) - s(2). What does this represent? b) Find the average rate of change of distance with respect to time as t changes from t1 = 2 to t2 = 5. This is the average velocity over those hours.

Learn how to calculate the average velocity for the function s(t) = 40t^1.2 over the interval [2,5]. This problem involves finding the total distance traveled and applying the formula for average velocity. Suitable for high school and early university students studying calculus.

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