# Chapter 4 - Problems - Page 148: 20

(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.

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