Acceleration question - confused as it is missing time

Question

An electron in a TV tube emitted from rest from a hot cathode reaches a velocity of 10ms-1 when it passes the anode. Find the acceleration of the electron if the cathode and anode are separated by 3 cm.

Answer 1

We are missing time, but we can still solve this. Assuming the acceleration is constant, we should be able to figure out what it is since they do tell us how far in distance was traveled to reach that certain velocity. You should've learned four kinematic equations, keep them close by. They are all unique in that they are missing a specific variable while still showing a relationship between the other four:

1. Δx = v₀t + (1/2)at²  , if you don't care about the final velocity
2. Δx = [(v₀ + v_f)/2]t   , if you don't care about the acceleration
3. v_f = v₀ + at             , if you don't care about the displacement (ie, change in position)
4. v_f² = v₀² + 2aΔx      , if you don't care about the time interval

Because we do not know the time variable and we don't need to know it, we will go with equation #4. Starting from there, we will isolate the variable we are solving for before before plugging in numbers, as this is the best physics practice:

v_f² = v₀² + 2aΔx

2aΔx = v_f² - v₀²

a = (v_f² - v₀²)/2Δx

Plugging in our values, we get:

a = [(10m/s)² - (0m/s)²]/2×3cm

a = [100m²/s²]/.06m

a = 1666.67 m/s²

Note that I wasn't sure what you meant by 10ms-1, so I just used v_f = 10m/s, but plug in your values accordingly. Hope this helps!