A particle shows a distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
A
B
B
C
C
D
D
A
Step-by-Step Solution
Concept: Instantaneous velocity is defined as the rate of change of position with respect to time (v=dtdx). Geometrically, this corresponds to the slope of the tangent to the position-time (or distance-time) curve at any given instant .
Analysis: To find the maximum instantaneous velocity, we must identify the point on the curve where the slope of the tangent is the steepest (maximum).
Observation: Comparing the slopes at points A, B, C, and D, the curve rises most steeply at point C. Therefore, the slope, and consequently the instantaneous velocity, is maximum at point C.
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