#### Answer

The magnitude of the centripetal acceleration is equal to the tangential acceleration after 8.2 seconds.

#### Work Step by Step

The tangential acceleration is $1.5~m/s^2$. We can find the speed $v$ when the centripetal acceleration is $1.5~m/s^2$.
$a_c = \frac{v^2}{r} = 1.5~m/s^2$
$v = \sqrt{(1.5~m/s^2)(r)}$
$v = \sqrt{(1.5~m/s^2)(100~m)}$
$v = 12.25~m/s$
We can find the time it takes to reach this speed.
$t = \frac{v-v_0}{a}$
$t = \frac{12.25~m/s-0}{1.5~m/s^2}$
$t = 8.2~s$
The magnitude of the centripetal acceleration is equal to the tangential acceleration after 8.2 seconds.