The acceleration of a $1971$ AMC Gremlin is defined by the relation a $=3$e$-0\mathrm{.}2$t $,$ where a and t are

expressed in ft$/$s$2$ and s$,$ respectively. Assume the gremlin starts at rest and x $=0$ and t $=0,$

determine the velocity and position at t$=0\mathrm{.}5$ s$.$ Also, what is the Gremlin$$s maximum velocity?

$[$Answers: at t$=0\mathrm{.}5$ s$,$ v$=1\mathrm{.}427$ ft$/$s$,$ x $=0\mathrm{.}363$ ft; max speed is $15$ ft$/$s