Answer
$m/s^2$
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 c * $t^2$ and we know that $t^2 $ will have units of $s^2$ and we know that overall $ct^2$ must have units of meters, then we have the following:
$ m = c * s^2 $ and therefore, c has units of $m/s^2$
