1. The problem is to find the average speed over given time intervals using the formula for average speed: $$\text{Average Speed} = \frac{\text{Change in Position}}{\text{Change in Time}} = \frac{\Delta s}{\Delta t}$$ 2. For the interval $t=0$ to $t=1$, the average speed is given as: $$\frac{5 - 0}{1 - 0} = 5$$ 3. For the interval $t=1$ to $t=2$, we need to calculate the average speed. Suppose the position at $t=1$ is $5$ and at $t=2$ is $7$ (inferred from the next interval calculation). Then: $$\text{Average Speed} = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2$$ 4. For the interval $t=2$ to $t=3$, the average speed is given as: $$\frac{10 - 7}{3 - 2} = \frac{3}{1} = 3$$ 5. Summary of average speeds: - $t=0$ to $t=1$: 5 - $t=1$ to $t=2$: 2 - $t=2$ to $t=3$: 3 This shows how to calculate average speed by dividing the change in position by the change in time for each interval.