Answer
$t = 3.0\times 10^{-9}~s$
Work Step by Step
We can find the acceleration of the electron:
$F = ma$
$\vert q \vert~E = ma$
$a = \frac{\vert q \vert~E}{m}$
$a = \frac{(1.6\times 10^{-19}~C)(5.0\times 10^4~N/C)}{9.1\times 10^{-31}~kg}$
$a = 8.79\times 10^{15}~m/s^2$
We can find the time it takes to travel 4.0 cm:
$y = \frac{1}{2}at^2$
$t^2 = \frac{2y}{a}$
$t = \sqrt{\frac{2y}{a}}$
$t = \sqrt{\frac{(2)(4.0\times 10^{-2}~m)}{8.79\times 10^{15}~m/s^2}}$
$t = 3.0\times 10^{-9}~s$
