vmstat vs uptime?

what is the relation between the output of vmstat
(cpu/us, cpu/sy, cpu/id) and output of uptime command?

it is said that
"one can think of load average as a percentage of system
utilization during the respective time period"
i have load average values obtained from uptime command
they are varying between 0-4.4 and i have output values for
vmstat it is constant for all (user %2,system %1 and idle %40)

measurements are done for 3.5 hours period.
do you have any idea?

Are you running the vmstat like this?

while true; do
   vmstat
   sleep 300 # measure every five min or something similar
done

If you are, then that's your problem right there. From the vmstat man page:

This figure will hardly change over 3.5 hours (especially if your system has an uptime that can be measured in months).

unfortunately i have used vmstat as you said,
that explains why cpu usage is constant.

but there is one more point that i didnt understand,
vmstat displayed varying output for free pages, and for page faults
according to my measurement. why?