A light–rail commuter train draws 635 A of 640–V DC electricity when accelerating. What is its power consumption rate in kilowatts?

(in kW) 406 kW
You are correct.

How long does it take to reach 30.0 m/s starting from rest if its loaded mass is 4.90×104 kg, assuming 93.0% efficiency and constant power?
(in s) 58.3 s
You are correct.

Find its average acceleration.
(in m/s^2) 0.514 m/s^2
You are correct.

What is the ratio of the acceleration you found for the light–rail train compares to what might be typical for an automobile? (A typical automobile can accelerate from 0 to 60 mph in 10 s.)

Need help with the last question please! I found the automobiles acceleration to be 2.778 and I divided that by the acceleration i found for the train:
2.778/.514=5.40 but it isn't the right answer. What am I doing wrong?

To find the ratio of the acceleration of the light-rail train compared to a typical automobile, you need to compare the magnitudes of the accelerations.

First, convert the acceleration of the automobile from mph to m/s:
60 mph = 26.8 m/s (rounded to two decimal places)

Now, calculate the ratio:
Ratio = Acceleration of automobile / Acceleration of light-rail train
= 26.8 m/s / 0.514 m/s^2
≈ 52.12

Therefore, the correct ratio is approximately 52.12.

To find the ratio of the acceleration of the light-rail train to that of a typical automobile, you need to calculate the ratio of the magnitudes of the two accelerations.

To start, convert the acceleration of the typical automobile from 0 to 60 mph in 10 s to meters per second squared (m/s^2).

1 mph is equal to 0.44704 m/s.
So, 60 mph is equal to 26.8224 m/s.

The acceleration of the automobile is found by dividing the change in velocity by the time:
Acceleration = (26.8224 m/s - 0 m/s) / 10 s = 2.68224 m/s^2.

Now, calculate the ratio of the accelerations:
Ratio = Acceleration of automobile / Acceleration of train

Ratio = 2.68224 m/s^2 / 0.514 m/s^2 = 5.216

Therefore, the correct ratio of the acceleration of the light-rail train compared to that of a typical automobile is 5.216.