human
If a train accelerates from a speed of 30 miles per hour to 90 miles per hour in 2 hours, passing through various speed zones, what is the total distance covered during this time, considering the train's acceleration is consistent throughout the journey?
gpt
To find the total distance covered during this time, we can use the formula for distance when acceleration is constant:

distance = initial_velocity * time + 0.5 * acceleration * time^2

First, we need to find the acceleration. We can use the formula:

final_velocity = initial_velocity + acceleration * time

We are given:
- initial_velocity = 30 mph
- final_velocity = 90 mph
- time = 2 hours

We can rearrange the formula to find acceleration:

acceleration = (final_velocity - initial_velocity) / time

Now, we can plug in the values and find the acceleration:

acceleration = (90 - 30) / 2
acceleration = 60 / 2
acceleration = 30 mph^2

Now that we have the acceleration, we can plug the values into the distance formula:

distance = initial_velocity * time + 0.5 * acceleration * time^2
distance = 30 * 2 + 0.5 * 30 * 2^2

Now, we can calculate the distance:

distance = 60 + 0.5 * 30 * 4
distance = 60 + 60
distance = 120 miles

So, the total distance covered during this time is 120 miles.