For which of the following graphs the average velocity of a particl moving along a straight line for time interval `(0,t)` must be negative`-`

Options

A.
B.
C.
D.

Explanation

To determine which graph indicates that the average velocity of a particle moving along a straight line for the time interval (0, t) must be negative, we need to analyze the concept of average velocity and how it relates to displacement.

### Step-by-Step Solution:

1. **Understanding Average Velocity**:
- Average velocity (V_avg) is defined as the total displacement (Δs) divided by the total time (Δt).
- Mathematically, it is expressed as:
\[ V_{avg} = \frac{\Delta s}{\Delta t} \]

2. **Identifying Displacement**:
- Displacement (Δs) is the change in position of the particle from the initial position (s(0)) to the final position (s(t)).
- If the final position is less than the initial position, then Δs will be negative.

3. **Analyzing Graphs**:
- We need to look for a graph where the position of the particle decreases over the time interval from 0 to t.
- This means that the graph should show a downward trend or a slope that is negative.

4. **Graph Interpretation**:
- If the graph of position vs. time shows that the particle moves from a higher position to a lower position, the displacement (Δs) will be negative.
- Therefore, if Δs is negative and Δt is always positive (since time cannot be negative), the average velocity will also be negative.

5. **Conclusion**:
- The graph that shows a downward slope from left to right indicates that the average velocity for the interval (0, t) must be negative.