### Problem 16: Displacement and Average VelocityThe displacement (in feet) of a particle moving in a straight line is given by the equation:\[ s = \frac{1}{2}t^2 - 6t + 23 \]where \( s \) is the displacement in feet and \( t \) is the time in seconds.#### (a) Find the average velocity over each time interval:1. **Interval [4, 8]**2. **Interval [6, 8]**3. **Interval [8, 10]**4. **Interval [8, 12]**#### Definitions and Formulae:The average velocity \( v_{avg} \) over a given time interval \([t_1, t_2]\) can be calculated using the formula:\[ v_{avg} = \frac{s(t_2) - s(t_1)}{t_2 - t_1} \]where:- \( s(t) \) represents the displacement at a particular time \( t \).- \( t_1 \) and \( t_2 \) are the start and end times of the interval, respectively.#### Steps to Calculate Average Velocity:1. **Identify the displacement at the start and end times for each interval.**2. **Plug in these displacement values and the time values into the average velocity formula.**3. **Calculate the average velocity for each interval.**Let's illustrate the process using the given time intervals:To find \( s(t) \) for any value of \( t \), substitute \( t \) into the displacement equation \( s = \frac{1}{2}t^2 - 6t + 23 \).For each interval:- Compute \( s(t_1) \)- Compute \( s(t_2) \)- Use the difference \(\frac{s(t_2) - s(t_1)}{t_2 - t_1} \) to find \( v_{avg} \).This procedure should be followed for each of the given time intervals: \([4, 8]\), \([6, 8]\), \([8, 10]\), and \([8, 12]\).

Name: ### Problem 16: Displacement and Average VelocityThe displacement (in
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: ### Problem 16: Displacement and Average VelocityThe displacement (in feet) of a particle moving in a straight line is given by the equation:\[ s = \frac{1}{2}t^2 - 6t + 23 \]where \( s \) is the displacement in feet and \( t \) is the time in secon