One of the world's fastest roller coasters is located in a theme park in Valencia, California. Riders go from 0 to 100 miles per hour in 7 seconds. Find the acceleration of the roller coaster during this time interval in miles per second squared.
acceleration = change in velocity/change in time
= 100 miles per hour/7 second
= (100 miles per 3600 seconds)/7 seconds
= 100 miles/25200 sec^2
= .004 miles/sec^2 (correct to 3 decimals)
To find the acceleration of the roller coaster during the given time interval, you need to use the formula for acceleration:
Acceleration (a) = Change in velocity (Δv) / Time interval (Δt)
In this case, the change in velocity is from 0 mph to 100 mph, which is 100 mph. The time interval is 7 seconds.
To convert 100 mph to miles per second, you need to divide by the number of seconds in an hour. There are 60 minutes in an hour and 60 seconds in a minute, so there are 60 x 60 = 3600 seconds in an hour.
Thus, 100 mph is equal to 100/3600 = 0.0278 miles per second.
Now we can calculate the acceleration:
Acceleration = Δv / Δt
Acceleration = 0.0278 miles per second / 7 seconds
Acceleration ≈ 0.00397 miles per second squared
Therefore, the acceleration of the roller coaster during this 7-second interval is approximately 0.00397 miles per second squared.