An electron of mass 9.11 10-31 kg has an initial speed of 2.85 105 m/s. It travels in a straight line, and its speed increases to 6.93 105 m/s in a distance of 5.50 cm. Assume its acceleration is constant.

To find the acceleration of the electron, we can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (6.93 * 10^5 m/s)
u = initial velocity (2.85 * 10^5 m/s)
a = acceleration (unknown)
s = distance (5.50 cm)

Converting the distance to meters:
s = 5.50 cm = 5.50 * 10^-2 m

Substituting the given values into the equation, we have:
(6.93 * 10^5 m/s)^2 = (2.85 * 10^5 m/s)^2 + 2a * (5.50 * 10^-2 m)

Simplifying the equation:
(4.80 * 10^11 m^2/s^2) = (8.12 * 10^10 m^2/s^2) + 2a * (5.50 * 10^-2 m)

Rearranging the equation to solve for acceleration:
2a * (5.50 * 10^-2 m) = (4.80 * 10^11 m^2/s^2) - (8.12 * 10^10 m^2/s^2)

2a * (5.50 * 10^-2 m) = (3.99 * 10^11 m^2/s^2)

Dividing both sides of the equation by 2 * (5.50 * 10^-2 m), we get:
a = (3.99 * 10^11 m^2/s^2) / (2 * 5.50 * 10^-2 m)

a ≈ 1.82 * 10^14 m/s^2

The acceleration of the electron is approximately 1.82 * 10^14 m/s^2.

To determine the acceleration, we can use the equation for average acceleration:

acceleration (a) = (final velocity - initial velocity) / time

In this case, the time is not given directly, but we can find it using the equation for distance traveled with constant acceleration:

distance (d) = (initial velocity * time) + (0.5 * acceleration * time^2)

Simplifying this equation, we get:

d = initial velocity * time + (0.5 * acceleration * time^2)

Rearranging the equation, we can solve for time:

0.5 * acceleration * time^2 + initial velocity * time - d = 0

This equation is a quadratic equation, which can be solved using the quadratic formula:

time = (-initial velocity ± sqrt((initial velocity)^2 - 4 * 0.5 * acceleration * (-d))) / (2 * 0.5 * acceleration)

Plugging in the given values:

initial velocity = 2.85 * 10^5 m/s
final velocity = 6.93 * 10^5 m/s
distance = 5.50 cm = 0.055 m

We have two unknowns: acceleration and time. To find the acceleration, we need to solve for time first.

Let's calculate the value inside the square root first:

(initial velocity)^2 - 4 * 0.5 * acceleration * (-d)
= (2.85 * 10^5)^2 - 4 * 0.5 * acceleration * (-0.055)

Now, we can put the values into the quadratic formula:

time = (-2.85 * 10^5 ± sqrt((2.85 * 10^5)^2 - 4 * 0.5 * acceleration * (-0.055))) / (2 * 0.5 * acceleration)

Since it travels in a straight line and its speed increases, we know the acceleration is positive.

After solving for time using both the positive and negative signs in the quadratic formula, we can substitute the obtained values into the equation for average acceleration to find the acceleration.