Electron acceleration

Question:

If you have an electron with a start velocity of 0 ms^-1 and an end velocity of 10⁷ ms^-1 and it has travelled 3m. What is its acceleration?

Answer

Use v = 10 000 000 ms^-1 and u = 0 ms^-1.
Now there are four of the following quantities in all the equations of motion (except the one for constant velocity) u,v,s,a and t.

1. Check which of these you have
You have v,u and s
2. Decide which one you need
You want the acceleration (a).

Next step.

3. Choose the right equation! It must involve u,v,s and a.
The one you need is v² = u² + 2as
Putting the numbers in here gives: a = v²/2s = 10¹⁴/2x3 = 1.67x1013 ms^-2.

If you don't know the equation that I have used then you will have to do it in three steps.

1. Find the average velocity = [10 000 000 - 0]/2 = 5 000 000 ms^-1
2. Use: Distance = average velocity x Time to give
Time(t) = 3/5000000 = 0.000 000 6 s
3. Now use: Acceleration (a) = [v-u]/t to give
a = 10 000 000/0.000 000 6 = 1.67x10¹³ ms^-2.