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?

1 Answer
Sep 7, 2015

Answer:

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#