A particle moves along a straight line so that its displacement from a fixed point O…

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

A particle moves along a straight line so that its displacement from a fixed point O at time

t

seconds is given by

s(t)=3t^{3}-5t^{2}+2t+7\ \text{(metres)}.

(i) Find the expression for the velocity

v(t)

of the particle. (ii) Calculate the instantaneous velocity at

t=2\text{ s}

. (iii) Determine the average velocity of the particle during the interval

1\text{ s}\le t\le2\text{ s}

and compare this value with the instantaneous velocity obtained at the beginning of that interval,

t=1\text{ s}