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# In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude $4.0 \times 10 ^ { 5 } \mathrm { N } / \mathrm { C }$ during the first 5.0 cm of the tube's length; then they move at essentially constant velocity another 45 cm before hitting the screen. (a) Find the speed of the electrons when they hit the screen. (b) How long does it take them to travel the length of the tube?

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### 1 Concepts and Principles

1- The $\textbf{magnitude of the acceleration}$ of a particle of charge $\textcolor{black}{q}$ and mass $\textcolor{black}{m}$ moving in an electric field of magnitude $\textcolor{black}{E}$ is:

$\begin{equation*} a=\dfrac{|q|E}{m}\tag{1} \end{equation*}$

2- $\textbf{Particle Under Constant Acceleration}$: If a particle moves in a straight line with a constant acceleration $a_x$, its motion is described by kinematics equations, from which we will use the following equation:

$\begin{gather*} v_{xf}^2=v_{xi}^2+2a_x \Delta x\tag{2} \\\\ \Delta x=v_{xi}t+\dfrac{1}{2}a_x t^2 \tag{3} \end{gather*}$

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