The position of a pinewood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of the car for (a) the first second, (b) the last $3\mathrm{s}$, and (c) the entire period of observation.

Key Concepts: Average Velocity, Position-Time Graph Explanation: To find the average velocity, we need to use the formula: average velocity = total displacement / total time. We can find the displacement of the car by subtracting the initial position from the final position. The total time is just the difference between the final and initial times. To find the displacement and time intervals for different time periods, we need to plot a position-time graph. Step by Step Solution: Step 1. Plot the position-time graph using the data provided in the table Step 2. Calculate the displacement and time interval for the first second and find the average velocity using the formula. average velocity = total displacement / total time. Step 3. Calculate the displacement and time interval for the last 3s and find the average velocity using the formula. average velocity = total displacement / total time. Step 4. Calculate the displacement and time interval for the entire period of observation and find the average velocity using the formula. average velocity = total displacement / total time. Final Answer: a) 4.5 ft/s, b) -1.5 ft/s, c) 0.375 ft/s