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.
Math - Reiny, Monday, March 8, 2010 at 9:46am
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
why was the numerator and denominator multiplied by 3600
the original velocity was in miles/hour
but the question asked for miles/second
how many seconds are there in an hour?
Because there are 3600 seconds in one hour, so multiplying the numerator and denominator by 3600 allows us to convert 100 miles per hour to miles per second. Basically, we're converting the units from hours to seconds so that the numerator and denominator have the same units.
The numerator and denominator were multiplied by 3600 because 1 hour is equal to 3600 seconds. By multiplying the numerator and denominator by 3600, we are converting the velocity from miles per hour to miles per second. This allows us to maintain consistent units when calculating the acceleration.
The numerator and denominator were multiplied by 3600 to convert the time interval from seconds to hours.
In the given problem, the velocity of the roller coaster is given in miles per hour, and the acceleration needs to be calculated in miles per second squared. To do this, we need to ensure that the time interval is in seconds instead of hours.
Multiplying the numerator and denominator by 3600 allows us to convert 1 hour (which is equal to 3600 seconds) into seconds. This conversion ensures that the units on both the numerator and denominator are the same, so they can be cancelled out.
By multiplying the numerator by 3600, we have converted miles per hour to miles per 3600 seconds. Then, when we divide this value by 7 seconds (the given time interval), we get the acceleration in miles per second squared.