Finding the Vectorized Way to Perform FOR Loops with Calculation Between Rows

Finding the Vectorized Way to Perform FOR Loops with Calculation Between Rows

I'm trying to find a vectorized procedure that can replace the following
code (which takes a LONG time to run):
for (i in 2:nrow(z)) {
if (z$customerID[i]==z$customerID[i-1])
{z$timeDelta[i]<-(z$time[i]-z$time[i-1])} else {z$timeDelta[i]<- NA}
}
I tried looking for different apply snippets, but haven't found anything
useful.
Thanks in advance!
Yoni
EDIT: Sample Data:
customerID time
1 2013-04-17 15:30:00 IDT
1 2013-05-19 11:32:00 IDT
1 2013-05-20 10:14:00 IDT
2 2013-03-14 18:41:00 IST
2 2013-04-24 09:52:00 IDT
2 2013-04-24 17:08:00 IDT
And I want to get the following output:
customerID time timeDelta*
1 2013-04-17 15:30:00 IDT NA
1 2013-05-19 11:32:00 IDT 31.83
1 2013-05-20 10:14:00 IDT 0.94
2 2013-03-14 18:41:00 IST NA
2 2013-04-24 09:52:00 IDT 40.59
2 2013-04-24 17:08:00 IDT 0.3
*I prefer the time will be in days