Question

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

Answer 1

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

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.

`106 years * (86,400 universe-seconds)/(1,010 years)=9,067.728 s`

That is about 2 and half hours.