Solving for Electron Acceleration and Time in a Television Tube - Homework Help

[elimenohpee]

Homework Statement

In a television tube, electrons travel down the tube and strike the fluorescent material at
the end of the tube. Their impact with this material causes light to be emitted, thereby producing
the picture we see. The electrons are accelerated from rest to a speed of 2 x 108 ms-1 in a distance
of 1.50 cm.
(i) What is the acceleration of an electron during this process? (10 marks)
(ii) How long does the acceleration take?

Homework Equations

(i) the acceleration I calculated seems WAY too large. I know the acceleration will be big, but I didn't think it could exceed the speed of light due to the theory of relativity.

(ii) the time to accelerate makes sense, but I think its wrong because I calculated the acceleration wrong.

The Attempt at a Solution

(i) I used the equation that doesn't involve time, only velocity, initial velocity, position and time:
v^2 = v^2(0) + 2a (x - x0)
(2*10^8)^2 = 0 + 2a (0.015m - 0)
a = 1.3 * 10^18 ?

(ii) with a = 1.3 * 10^18, I just plugged it into x = 0.5a(t^2), solved for t and got t = 1.5 * 10^-10 s

 

[Delphi51]

Extremely large accelerations do happen in these tubes.
But the speed given in the question - more than half the speed of light - indicates you should be using relativity formulas instead of Newtonian ones.

Can you teach me how to do this?
If you aren't in a relativity class, maybe you aren't supposed to worry about relativity.

 

[elimenohpee]

Its not in a relativity class, its just an introductory course to Newtonian physics. I know we aren't supposed to know about relativity at this point, but that acceleration just didn't make sense to me. Can anyone verify if this is right?

 

[Delphi51]

I haven't gone through all the calculator work, but it certainly appears to be correct and the acceleration is reasonable. In a non-relativity course, you have it done correctly.