Motion in a Straight Line - Result Question 19

19.

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

[2008]

(a) $B$

(b) $C$

(c) $D$

(d) $A$

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Answer:

Correct Answer: 19. (b)

Solution:

  1. (b) The slope of the graph $\frac{d s}{d t}$ is maximum at $C$ and hence the instantaneous velocity is maximumat $C$.

Instantaneous velocity,

$ \vec{v} _{\text{ins }}=\lim _{\Delta t \to 0} \frac{\Delta \vec{s}}{\Delta t}=\frac{d \vec{s}}{d t}$ The instantaneous velocity of an object at a given instant is first derivative of displacement with respect to time.

The slope of displacement-time graph at any instant of time gives the measure of instantanesous velocity of an object at that instant.