Answer
$a = 1.94~m/s^2$
Work Step by Step
We can find the speed after $15.0~s$:
$v = a~t$
$v = (0.500~m/s^2)(15.0~s)$
$v = 7.50~m/s$
We can find the centripetal acceleration:
$a_c = \frac{v^2}{r}$
$a_c = \frac{(7.50~m/s)^2}{30.0~m}$
$a_c = 1.875~m/s^2$
We can find the net linear acceleration:
$a = \sqrt{(1.875~m/s^2)^2+(0.500~m/s^2)^2}$
$a = 1.94~m/s^2$
