A particle moves along a straight track

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A particle moves along a straight track. Its velocity at time

t

seconds is given by

v(t)=6t^{2}-4t+1\;\text{m s}^{-1},

and its position at

t=0

3\;\text{m}

from a fixed origin. (a) Find the position function

s(t)

of the particle. (b) Determine the acceleration of the particle at

t=2\text{ s}

. (c) Compute the total displacement of the particle during the first

3

seconds of motion.