Answer
$m/s^3$
Work Step by Step
The position is given by $x=ct^2−bt^3 $where x is in meters and t is in time. Since x is in meters, then we know that each of the terms on the right side (since they are subtracted), must have the same units, and must also be in meters.
Since we have $bt^3$ and we know that $t^3$ will have units of $s^3$ and we know that overall $bt^3$ must have units of meters, then we have the following:
$ m = b*s^3 $ and therefore b has units of $m/s^3$
