1. **Problem Statement:** Find the instantaneous velocity of the motorcyclist at time $t=3$ seconds given the position data. 2. **Understanding Instantaneous Velocity:** Instantaneous velocity at a time $t$ is the limit of the average velocity over an interval as the interval shrinks to zero around $t$. Since we have discrete data, we approximate it by calculating average velocities over intervals close to $t=3$. 3. **Formula for Average Velocity:** $$\text{Average velocity} = \frac{\text{Change in position}}{\text{Change in time}} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}$$ 4. **Calculate average velocities around $t=3$:** - Interval [2,3]: $$\frac{23.2 - 10.7}{3 - 2} = \frac{12.5}{1} = 12.5\ \text{ft/s}$$ - Interval [3,4]: $$\frac{50.4 - 23.2}{4 - 3} = \frac{27.2}{1} = 27.2\ \text{ft/s}$$ 5. **Approximate instantaneous velocity at $t=3$:** Take the average of the two average velocities around $t=3$: $$\frac{12.5 + 27.2}{2} = \frac{39.7}{2} = 19.85\ \text{ft/s}$$ 6. **Answer:** The instantaneous velocity at $t=3$ seconds is approximately **19.85 ft/s**.