An electron is accelerated by a constant electric field of magnitude 325 N/C.

(a) Find the acceleration of the electron. (m/s^2)
(b) Use the equations of motion with constant acceleration to find the electron's speed after 1.05 10-8 s, assuming it starts from rest. (m/s)

m•a=e•E,

a = e•E/m = 1.6•10^-19•325/9.1•10^-31 = …
v = a•t = ...

To find the acceleration of the electron, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object times its acceleration:

F = m * a

In this case, we know the magnitude of the electric field acting on the electron, which is given as 325 N/C. The force exerted on the electron is the product of the electric field strength and the charge of the electron:

F = q * E

where q is the charge of the electron. The charge of an electron is -1.6 * 10^-19 C (coulombs). Therefore, we can rewrite the equation as:

q * E = m * a

Now, we can solve for the acceleration (a):

a = (q * E) / m

where m is the mass of an electron, which is 9.1 * 10^-31 kg.

Let's plug in the values and calculate:

a = (-1.6 * 10^-19 C) * (325 N/C) / (9.1 * 10^-31 kg)
a ≈ -57.7 * 10^11 m/s^2

Since the value is negative, it means that the acceleration is in the opposite direction of the electric field. But magnitude-wise, the acceleration is approximately 57.7 * 10^11 m/s^2.

Now, let's move on to part (b).

To find the speed of the electron after a given time using the equations of motion with constant acceleration, we can use the following equation:

v = u + a * t

where:
v is the final velocity (speed),
u is the initial velocity (speed),
a is the acceleration,
t is the time.

In this case, the electron starts from rest, so the initial velocity (u) is zero. Therefore, the equation becomes:

v = 0 + a * t

Now, let's plug in the values we have:

t = 1.05 * 10^-8 s
a = -57.7 * 10^11 m/s^2 (negative sign indicates opposite direction of acceleration)

v = 0 + (-57.7 * 10^11 m/s^2) * (1.05 * 10^-8 s)
v ≈ -6.05 * 10^3 m/s

Again, the value is negative, indicating that the electron is moving in the opposite direction of the electric field. But magnitude-wise, the speed of the electron after 1.05 * 10^-8 seconds is approximately 6.05 * 10^3 m/s.

(a) To find the acceleration of the electron, we can use the equation:

acceleration = electric field / charge of electron

The charge of an electron is known to be -1.6 x 10^-19 C. Therefore, we have:

acceleration = 325 N/C / (-1.6 x 10^-19 C)

Calculating the acceleration:

acceleration = -2.03125 x 10^21 m/s^2

Therefore, the acceleration of the electron in this electric field is approximately -2.03125 x 10^21 m/s^2.

(b) Using the equations of motion with constant acceleration, we can find the electron's speed after a given time. Assuming the electron starts from rest (initial velocity = 0), we can use the equation:

final velocity = initial velocity + (acceleration × time)

Plugging in the known values:

acceleration = -2.03125 x 10^21 m/s^2
time = 1.05 x 10^-8 s

final velocity = 0 + (-2.03125 x 10^21 m/s^2 × 1.05 x 10^-8 s)

Calculating the final velocity:

final velocity = -2.1328125 x 10^13 m/s

Therefore, the electron's speed after 1.05 x 10^-8 s, assuming it starts from rest, is approximately -2.1328125 x 10^13 m/s.

Note: The negative sign indicates that the electron is moving in the opposite direction of the electric field.