The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is

Question

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

Accepted Answer

1. **Definition of Instantaneous Velocity:** The instantaneous velocity ($v$) of a particle is defined as the rate of change of position with respect to time, given by the derivative $v = \frac{dx}{dt}$ .
2. **Graphical Interpretation:** On a displacement-time ($x-t$) graph, the value of $\frac{dx}{dt}$ at any specific instant corresponds to the **slope of the tangent** to the curve at that point .
3. **Analyzing Slope Signs:**
   - A **positive slope** (tangent pointing up) indicates positive velocity.
   - A **zero slope** (horizontal tangent) indicates zero velocity.
   - A **negative slope** (tangent pointing down) indicates negative velocity.
4. **Conclusion:** To find the point where velocity is negative, one must identify the point on the graph where the tangent has a negative slope (i.e., the curve is going downwards). Point E corresponds to a region where the displacement is decreasing with time, meaning the slope is negative.

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