Two flat metal plates, 2.0 cm apart, carry opposite charges and make a uniform field of 2.5 × 10³…

Step 1. The acceleration. $a = \dfrac{eE}{m} = \dfrac{1.6 \times 10^{-19}\ \text{C} \times 2.5 \times 10^{3}\ \text{N/C}}{9.1 \times 10^{-31}\ \text{kg}} = 4.40 \times 10^{14}\ \text{m/s}^2$.

Step 2. The time. From rest, $d = \tfrac{1}{2}at^2$. We want $t$, so $t = \sqrt{\dfrac{2d}{a}} = \sqrt{\dfrac{2 \times 0.020\ \text{m}}{4.40 \times 10^{14}\ \text{m/s}^2}} = 9.54 \times 10^{-9}\ \text{s}$, that is $9.54$ ns.

Step 3. The speed. $v = at = 4.40 \times 10^{14} \times 9.54 \times 10^{-9}\ \text{m/s} = 4.19 \times 10^{6}\ \text{m/s}$.