Final answer:
To find the electron's acceleration in a linear accelerator, we use the kinematic equation v^2 = 2as, considering an initial velocity of zero. The final velocity is 1.60% of the speed of light, and after substituting values and solving for acceleration, we find the electron's average acceleration is approximately 3.20 x 10^12 m/s^2.
Step-by-step explanation:
To calculate the electron's acceleration during the first 36.0 m of travel in a linear accelerator, we need to use kinematic equations. The electron reaches 1.60% of the speed of light, which is approximately 4.80 x 106 m/s (since the speed of light is roughly 3 x 108 m/s). We'll assume the electron starts from rest, which is a common assumption in these types of problems unless otherwise specified.
The kinematic equation that relates final velocity (v), initial velocity (u), acceleration (a), and displacement (s) is:
v2 = u2 + 2as
Since the initial velocity u is 0 (the electron starts from rest), the equation simplifies to:
v2 = 2as
Now we rearrange the equation to solve for acceleration a:
a = v2 / (2s)
Substituting in the values, we get:
a = (4.80 x 106 m/s)2 / (2 x 36.0 m)
After performing the calculations:
a ≈ 3.20 x 1012 m/s2
This is the average acceleration of the electron over the 36.0 m during which it is being accelerated.