The displacement of a particle as a function of time is shown in the figure. The figure shows that

Question

Accepted Answer

1. **Slope represents Velocity:** In a displacement-time ($x-t$) graph, the instantaneous velocity of the particle is defined as the slope of the tangent to the curve at any specific instant ($v = \frac{dx}{dt}$) .
2. **Graph Analysis:**
   - **Initial State:** The description implies the graph starts with a specific positive slope at $t=0$, indicating the particle has an initial non-zero velocity.
   - **Retardation:** As time increases, if the slope of the curve decreases (the curve becomes less steep), it indicates that the velocity is decreasing. A decreasing velocity signifies retardation (negative acceleration).
   - **Stopping:** Finally, if the tangent to the curve becomes horizontal (slope $= 0$), the velocity becomes zero, meaning the particle stops.
3. **Conclusion:** The option describing a particle starting with a velocity, undergoing retardation, and stopping corresponds to a graph with an initially positive slope that gradually decreases to zero.

Step-by-Step Solution

Practice All PHYSICS Questions