The graph you've provided shows the position $s(t)$ of an object in meters over time $t$ in seconds. To find the velocity, we need to calculate the slope (rate of change) of the position over time in each interval, as velocity is the derivative of the position function.

Here’s a breakdown of each time interval from the graph:

1. Interval $t = 0$ to $t = 1$

• Position goes from 0 meters to 4 meters.
• Slope (velocity) = $\frac{4 - 0}{1 - 0} = 4 \, \text{m/s}$.

2. Interval $t = 1$ to $t = 3$

• Position remains constant at 4 meters.
• Slope (velocity) = $\frac{4 - 4}{3 - 1} = 0 \, \text{m/s}$.

3. Interval $t = 3$ to $t = 4$

• Position drops from 4 meters to 1 meter.
• Slope (velocity) = $\frac{1 - 4}{4 - 3} = -3 \, \text{m/s}$.

4. Interval $t = 4$ to $t = 5$

• Position remains constant at 1 meter.
• Slope (velocity) = $\frac{1 - 1}{5 - 4} = 0 \, \text{m/s}$.

5. Interval $t = 5$ to $t = 6$

• Position increases from 1 meter to 5 meters.
• Slope (velocity) = $\frac{5 - 1}{6 - 5} = 4 \, \text{m/s}$.

6. Interval $t = 6$ to $t = 7$

• The graph ends at $t = 6$, so no data for this interval.

Velocity Graph

Now, to graph the velocity:

• From $t = 0$ to $t = 1$, velocity is $4 \, \text{m/s}$.
• From $t = 1$ to $t = 3$, velocity is $0 \, \text{m/s}$.
• From $t = 3$ to $t = 4$, velocity is $-3 \, \text{m/s}$.
• From $t = 4$ to $t = 5$, velocity is $0 \, \text{m/s}$.
• From $t = 5$ to $t = 6$, velocity is $4 \, \text{m/s}$.

Would you like a detailed sketch of the velocity graph or have further questions?

Here are 5 related questions:

1. How is the derivative related to the velocity in general?
2. What does the negative velocity indicate in this graph?
3. How would the acceleration graph look based on the velocity graph?
4. What real-world scenario could this graph represent?
5. Can you find the total displacement from the graph?

Tip: To find velocity from a position-time graph, remember that velocity is the slope of the graph at any point!