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