An electron with an initial speed of 4.56 x 10^5m/s enters the second section of a particle accelerator that is 3.50 cm long. In this section, the electron is accelerated to a speed of 3.25 x 10^6 m/s.

Question

Calculate the magnitude of the acceleration of this particle during the second stage.

Answer 1

To calculate the acceleration of the electron during the second stage of the accelerator, we can use the equation:

acceleration = (final velocity - initial velocity) / time

First, we need to calculate the time it took for the electron to accelerate in the second section. We can use the equation:

distance = initial velocity * time + 0.5 * acceleration * time^2

Since the initial distance is 0 and the acceleration is constant, we can simplify the equation to:

distance = initial velocity * time

3.50 cm = 4.56 x 10^5 m/s * time

Solving for time:

time = 3.50 cm / (4.56 x 10^5 m/s) = 7.67 x 10^-6 s

Now we can calculate the acceleration using the initial and final velocities and the time:

acceleration = (3.25 x 10^6 m/s - 4.56 x 10^5 m/s) / (7.67 x 10^-6 s)
acceleration = 2.794 x 10^6 m/s / 7.67 x 10^-6 s
acceleration = 3.64 x 10^11 m/s^2

Therefore, the magnitude of the acceleration of the electron during the second stage of the accelerator is 3.64 x 10^11 m/s^2.