The displacement (in feet) of a particle moving in a straight line is given by 
s = 
1
2
t2 − 5t + 15,
 where t is measured in seconds.
(a)
Find the average velocity (in ft/s) over each time interval.

The displacement of the particle is given by the function \( s(t) = \frac{1}{2}t^2 - 5t + 15 \), where \( s \) is the displacement in feet and \( t \) is the time in seconds. To find the average velocity over a time interval, we use the formula for average velocity:

\[
\text{Average velocity} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}
\]

where \( t_1 \) and \( t_2 \) are the endpoints of the time interval.

Could you specify the time intervals over which you would like to calculate the average velocity, or would you like to solve for a specific time range?

Let me know if you'd like more details, and here are five relative questions to expand on this topic:

1. What is the difference between average velocity and instantaneous velocity?
2. How would you find the instantaneous velocity at any given time for this particle?
3. What are some typical real-life applications of average velocity in physics?
4. Can you calculate acceleration from the displacement function, and if so, how?
5. How does changing the time interval affect the average velocity?

**Tip:** The slope of the secant line on a displacement-time graph between two points gives the average velocity over that interval.

The displacement (in feet) of a particle moving in a straight line is given by s = 1/2 t^2 − 5t + 15, where t is measured in seconds. (a) Find the average velocity (in ft/s) over each time interval.

Learn how to calculate the average velocity of a particle moving in a straight line, given the displacement function s = 1/2 t^2 - 5t + 15. This problem covers kinematics concepts, including quadratic functions and the secant line theorem. Suitable for high school students in Grades 10-12.

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