Question

An electron with initial velocity v0 = 1.10 × 10^5 m/s enters a region 1.0 cm long where it is electrically accelerated (see the figure). It emerges with velocity v = 5.37 × 10^6 m/s. What is its acceleration, assumed constant?

Answer 1

I found: `a=1.44xx10^15m/s^2`

Explanation:

I am going to use non-relativistic kinematics concepts here although the veleocities are quite high.

You can use the relationships:
`v_f=v_0+at`
`x_f-x_i=d=v_0t+1/2at^2`
where:
`d=1cm=0.01m` is the distance (linear) described;
`v` is velocity;
`a` is acceleration.
From the first we get:
`t=(v_f-v_0)/a=(5.37xx10^6-1.10xx10^5)/a=(5.26xx10^6)/a`
to simplfy let us set: `(5.26xx10^6)/a=k/a` and substitute into the second:
`0.01=1.10xx10^5*k/a+1/2cancel(a)k^2/a^cancel(2)`
rearranging and using our values:
`0.01a=1.10xx10^5*5.26xx10^6+1/2(5.26xx10^6)^2`
`a=1.44xx10^15m/s^2`