a) A unit of time sometimes used in microscopic physics is the shake. One shake equals 10–8 s. Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about 106 years, whereas the universe is about 1010 years old. If the age of the universe is defined as 1 "universe day," where a universe day consists of "universe seconds" as a normal day consists of normal seconds, how many universe seconds have humans existe

a) Yes, there are [tex]10^8[/tex] shakes in a second ([tex]1 s \frac{1 shake}{10^{-8}s}=10^8 shake[/tex]) in a year there are 31,536,000 seconds... that is 3.1536x[tex]10^7[/tex] ([tex]1year\frac{365 day}{1 year} \frac{24 h}{1 day} \frac{60 min}{1 h}\frac{60s}{1min}=3.1536 *10^7[/tex])

b) Note that the defined universe day will have 60*60*24=86400 universe seconds if the seconds are defined as normal seconds.

Also one universe day (or 86400 universe seconds) is equivalent to 1010 years. Now using a rule of three we can know the seconds that humans have existed.

[tex]106 years * \frac{86,400 universe-seconds}{1,010 years}=9,067.728 s[/tex]

That is about 2 and half hours.