Time difference calculations considering the midnight time using r - r

Question

I am working on a problem where I need to calculate the time difference in minutes. I have the time values in hh:mm:ss format in a column (more than 28,000 values).
I have been using the following function to calculate the time difference.
tdiff <- dt[dt, Time_Diff := c(abs(diff(as.numeric(Time))),0.30), Student_ID]
where dt --> is the ordered data table and
0.30 --> 30 minutes assigned to the last activity of the student in a course.
This works, but it is not considering the midnight time.
Thanks to #niko for his help and this problem is solved, however the '30 minutes' that should be assigned to each student's last activity is still not done. Any help in this direction will be greatly appreciated. Thank you.
The expected output is described below
S_Id Date Time Time_Diff Time_Diff(minutes)
A 10/08/2018 23:49:00 00:01:00 1 minutes
A 10/08/2018 23:50:00 00:09:00 9
A 10/08/2018 23:59:00 00:02:00 2
A 10/09/2018 00:01:00 00:09:00 9
A 10/09/2018 00:10:00 08:02:00 482
A 10/09/2018 08:12:00 04:08:00 248
A 10/09/2018 12:20:00 10:01:00 601
A 10/09/2018 22:21:00 01:35:00 95
A 10/09/2018 23:56:00 00:09:00 9
A 10/10/2018 00:05:00 00:05:00 5
A 10/10/2018 00:10:00 00:02:00 2
A 10/10/2018 00:12:00 00:30:00 30
B 10/08/2018 23:49:00 00:01:00 1
B 10/08/2018 23:50:00 00:09:00 9
B 10/08/2018 23:59:00 00:02:00 2
B 10/09/2018 00:01:00 00:09:00 9
B 10/09/2018 00:10:00 08:02:00 482
B 10/09/2018 08:12:00 04:08:00 248
B 10/09/2018 12:20:00 10:01:00 601
B 10/09/2018 22:21:00 01:35:00 95
B 10/09/2018 23:56:00 00:09:00 9
B 10/10/2018 00:05:00 00:05:00 5
B 10/10/2018 00:10:00 00:02:00 2
B 10/10/2018 00:12:00 00:30:00 30
C 10/08/2018 23:49:00 00:01:00 1
C 10/08/2018 23:50:00 00:09:00 9
C 10/08/2018 23:59:00 00:02:00 2
C 10/09/2018 00:01:00 00:09:00 9
C 10/09/2018 00:10:00 08:02:00 482
C 10/09/2018 08:12:00 04:08:00 248
C 10/09/2018 12:20:00 10:01:00 601
C 10/09/2018 22:21:00 01:35:00 95
C 10/09/2018 23:56:00 00:09:00 9
C 10/10/2018 00:05:00 00:05:00 5
C 10/10/2018 00:10:00 00:02:00 2
C 10/10/2018 00:12:00 00:30:00 30

Answer 1

Try converting date and time to POSIXct
# dt is your data frame
diff(as.POSIXct(paste(dt$Date, dt$Time), format='%m/%d/%Y %H:%M:%S')) # or '%d/%m/%Y %H:%M:%S'
That should do the trick.
Data
dt <- structure(list(Date = c("10/08/2018", "10/08/2018", "10/08/2018", "10/09/2018", "10/09/2018",
"10/09/2018", "10/09/2018", "10/09/2018", "10/09/2018", "10/10/2018",
"10/10/2018", "10/10/2018"),
Time = c("23:49:00", "23:50:00", "23:59:00", "00:01:00", "00:10:00", "08:12:00",
"12:20:00", "22:21:00", "23:56:00", "00:05:00", "00:10:00", "00:12:00")),
class = "data.frame", row.names = c(NA, -12L))