Mathematics

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. (a) Find the position function

s(t)

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

t=2\text{ s}

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

3

seconds of motion.