An electron in the cathode ray tube of a tele-

vision set enters a region where it acceler-
ates uniformly from a speed of 30100 m/s to
a speed of 3.82 × 106 m/s in a distance of
2.97 cm.
What is its acceleration?
Answer in units of m/s2

To find the acceleration of the electron, we can use the acceleration formula:

acceleration = (change in velocity) / (time)

However, the given information does not include the time it takes for the electron to accelerate. But we can still find the acceleration by using another equation that relates distance, initial velocity, final velocity, and acceleration:

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

In this case, we know the distance (2.97 cm), the initial velocity (30100 m/s), and the final velocity (3.82 × 10^6 m/s). We can rearrange the formula to solve for the acceleration:

distance = (initial velocity × time) + (0.5 × acceleration × time^2)
2.97 cm = (30100 m/s × time) + (0.5 × acceleration × time^2)

Now, let's convert the distance to meters and rearrange the equation:

0.0297 m = (30100 m/s × time) + (0.5 × acceleration × time^2)

Since we don't have the time, let's rearrange the equation again and solve for acceleration:

0.5 × acceleration × time^2 + (30100 m/s × time) - 0.0297 m = 0

Now, we can use the quadratic formula to solve for time:

time = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 0.5, b = 30100 m/s, and c = -0.0297 m.

Using these values, we can calculate time using the quadratic formula. Once we have the value of time, we can substitute it back into the equation to find the acceleration.