Don't you have another method

Step 1: Find displacement $s$ using the formula for constant acceleration from rest.
$s = \frac{1}{2} a t^{2}$

Step 2: Substitute $a = 2\ m/s^{2}$ and $t = 10\ \mathrm{s}$.
$s = \frac{1}{2} (2\ m/s^{2}) (10\ s)^{2}$
$s = (1\ m/s^{2}) (100\ s^{2})$
$s = 100\ m$

Step 3: Use the formula relating final velocity, initial velocity, acceleration, and displacement.
$v^{2} = u^{2} + 2 a s$

Step 4: Substitute $u = 0\ \mathrm{m/s}$, $a = 2\ m/s^{2}$, and $s = 100\ \mathrm{m}$.
$v^{2} = (0\ m/s)^{2} + 2 (2\ m/s^{2}) (100\ m)$
$v^{2} = 0 + 400\ m^{2/s^{2}}$
$v^{2} = 400\ m^{2/s^{2}}$

Step 5: Solve for $v$.
$v = \sqrt{400\ m^{2/s^{2}}}$
$v = 20\ m/s$

Final velocity: $\boxed{20\ m/s}$