Question

An electron in a cathode ray tube of a TV set enters a region where it accelerates uniformly from a speed of 3.1×104 m/s to a speed of 6.7×104 m/s in a distance of 2.0 cm. How long is the electron in the region where it accelerates?

Answer 1

This is a kinematics problem. Set up the constant acceleration equations via integration:
\[\frac{d^2x}{dt^2}=a\\\int\limits\frac{d^2x}{dt^2} dt=\int\limits a\ dt\\v=at+v_0\\\int\limits v\ dt=\int\limits (at+v_0)dt\\x=\frac{1}{2}at^2+v_0t+x_0\] Now you have two equations with two unknowns - 'a' the acceleration, and 't' the time span - so you should be able to solve this using algebra.

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