1. **Stating the problem:** We have a velocity-time equation given as $$v = \frac{9}{6} - \frac{2}{t}$$ and we want to find the time when the object changes direction and analyze the average speed over different intervals. 2. **Understanding the problem:** The object changes direction when velocity $$v$$ changes sign, i.e., when $$v=0$$. 3. **Set velocity to zero to find the time of direction change:** $$0 = \frac{9}{6} - \frac{2}{t}$$ 4. **Solve for $$t$$:** $$\frac{2}{t} = \frac{9}{6}$$ $$t = \frac{2}{\frac{9}{6}} = 2 \times \frac{6}{9} = \frac{12}{9} = \frac{4}{3}$$ 5. **Interpretation:** At $$t=\frac{4}{3}$$ seconds, the velocity is zero, so the object changes direction. 6. **Average speed over intervals:** - Average speed is the total distance divided by the time interval. - Since velocity changes sign at $$t=\frac{4}{3}$$, the average speed over intervals before and after this time will differ. 7. **Summary:** - The object changes direction at $$t=\frac{4}{3}$$ seconds. - Average speed calculations depend on the chosen time intervals relative to this point. This completes the analysis of the velocity-time equation and direction change.