Mathematics

Problem

A particle starts at position

s(0)=0

meters with initial velocity

v(0)=-1\,\text{m\,s}^{-1}

. Its acceleration is given by

a(t)=\begin{cases}2t,& 0\le t\le 2,\\-3,& 2< t\le6,\end{cases}

where

t

is in seconds and

a

in meters per second squared. (i) Determine the velocity

v(6)

of the particle. (ii) Determine the position

s(6)

of the particle.