# Time + Physics = I feel dumb

1. Jan 17, 2008

### AnkhUNC

1. The problem statement, all variables and given/known data

Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 97 centuries, what is the total (in hours) of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)?

2. Relevant equations

3. The attempt at a solution
I'm having a little trouble getting a grasp on what the question is actually asking. I'm assuming I need to take the 1 sec it changes per century, divide that by 100, then divide that by 365 to find the change per day correct? But I'm not sure even that is correct. I'm feeling a little lost.

2. Jan 17, 2008

### Dick

Your thoughts on starting are correct. Find the gain per day corresponding to 1ms/century and call it A. Then the gain after the first day is A, the gain after the second day is A+2A, the gain after the third is A+2A+3A. Etc etc. So you finally have A*(1+2+3+4...+N) where N is the number of days in 97 centuries. There is a simple formula for (1+2+3+4...+N) in terms of N. It's an arithmetic series.