Answer
(a) The speed of the electrons when they hit the screen is $1.7\times 10^6~m/s$
(b) It takes $t = 2.4\times 10^{-8}~seconds$ for the electrons to travel the length of the tube.
Work Step by Step
(a) We can find the acceleration of each electron:
$F = ma$
$a = \frac{F}{m}$
$a = \frac{6.4\times 10^{-17}~N}{9.1\times 10^{-31}~kg}$
$a = 7.0\times 10^{13}~m/s^2$
We can find the speed after moving a distance of 2.0 cm:
$v_f^2 = v_0^2+2ad$
$v_f = \sqrt{v_0^2+2ad}$
$v_f = \sqrt{0+(2)(7.0\times 10^{13}~m/s^2)(0.020~m)}$
$v_f = 1.7\times 10^6~m/s$
The speed of the electrons when they hit the screen is $1.7\times 10^6~m/s$
(b) We can find the time it takes to travel 2.0 cm in the tube:
$\Delta x = \frac{1}{2}at^2$
$t = \sqrt{\frac{2\Delta x}{a}}$
$t = \sqrt{\frac{(2)(0.020~m)}{7.0\times 10^{13}~m/s^2}}$
$t = 2.4\times 10^{-8}~s$
It takes $t = 2.4\times 10^{-8}~seconds$ for the electrons to travel the length of the tube.
