Consider a particle moving along a line with acceleration and initial velocity given by
\begin{align*} a(t) &= 1-2t\\ v(0) &= 6 \end{align*}
for \(0\leq t\leq 4\).
The velocity function of the particle as a function of \(t\) is
\[ v(t) = \answer {6-t^2+t}. \]
The total distance that the particle travels on the interval \([0,4]\) is \(\answer {\frac {49}{3}}\).
Note \(\displaystyle v(t)=-(t-3)(t+2)\) Therefore, \(v\) is
positive on \([0,3)\) and negative on \((3,4]\).