1. **State the problem:** We need to find the velocity at $3.5$ seconds from the given graphs.
2. **Identify the relevant graph:** Velocity is the rate of change of displacement with respect to time. The displacement graph is shown in Figure 7.2.
3. **Analyze the displacement graph at $3.5$ seconds:** From the description, displacement is constant from $0$ to $3$ seconds at $30$ m, then it decreases linearly from $3$ to $8$ seconds down to $0$ m.
4. **Calculate the velocity between $3$ and $8$ seconds:** Velocity is the slope of the displacement-time graph.
The slope $v = \frac{\Delta \text{displacement}}{\Delta \text{time}} = \frac{0 - 30}{8 - 3} = \frac{-30}{5} = -6$ m/s.
5. **Interpretation:** At $3.5$ seconds, which lies between $3$ and $8$ seconds, the velocity is constant and equals $-6$ m/s.
6. **Final answer:**
$$\boxed{v(3.5) = -6 \text{ m/s}}$$
This means the object is moving north to south (negative displacement direction) at $6$ meters per second at $3.5$ seconds.
Velocity 3.5S 1C4D1E
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.