A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the pa

Question

A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

Accepted Answer

1.  **Concept:** Instantaneous velocity is defined as the limit of the average velocity as the time interval tends to zero ($v = \lim_{\Delta t 	o 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$). Geometrically, this value at any instant is equal to the slope of the tangent drawn to the position-time (or distance-time) graph at that specific point .
2.  **Analysis:** To determine the point of maximum instantaneous velocity, one must identify where the slope of the curve is the steepest (maximum positive value).
3.  **Conclusion:** By observing the slope of the tangent at points A, B, C, and D, the curve is steepest at point C. Therefore, the instantaneous velocity is maximum at point C.

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