Which one is correct:
- Submit your work in time.
- Submit your work on time.
"In time" usually has an implicit "for (some event)", whereas "on time" means "before some deadline".
The "event" could be a deadline, but in that case "on time" is much more common.
"I got there in time for the parade"
"I delivered the report in time for him to read it before the meeting"
"I got to town in time (for)/(to catch) the last train"
"I got there in time" - meaning "in time for some event which is assumed to be known".
"I got there on time" - meaning "before the deadline" - which may be known to the hearer, but does not need to be, because the phrase itself implies a deadline as opposed to some other event.
On time means at a particular designated time, i.e. neither especially early nor late. The train is scheduled to arrive on time at 13:36.
In time means early enough, i.e. before a deadline or another cutoff. Passengers were required to be at the gate by 3:05pm; we didn't get to the airport till 3, but there was no line at security, so we still made it in time.
In this case, "on time" is the proper choice.
More details about the differences:
"In time" is used to suggest that I was able to perform an action before another event occurred:
I was able to reach you in time.
The difference between "in time" and "on time" would be deadlines or schedules that revolve around very specific date or hour:
The train was on time.
The project was completed on time.
Of note, the phrases can also be used in other unrelated contexts:
(in music) Step in time.
Dorian Gray was stuck in time.
Without further reference, on time is probably a better construction. A time has been set (a deadline) and the task will be done by then.
The project was scheduled for three months and it came in on time.
In time is usually used to refer to being completed in relation to something else.
I arrived at home in time to see my children before they left for school.
The two are both proper grammar. However, they carry different meanings. "Let the task be done on time." implies it to be completed by a certain time (usually a scheduled deadline) and no later. "Let the task be done in time." implies the task should be completed by the specified time.
Let's use different verbs: "Let the task be started on time." implies it to be started at a certain time and no earlier. "Let the task be started in time." implies the task should be started by the specified time and no later.
Because of limited context, it is hard to say which would fit this case better.
You would use "on time" to mean by a certain specific date an time. "In time" describes an event in which the chronology may not be that explicit.
Papers are due on 11/15 by noon. All students are expected to submit their papers on time.
Do you think we can get help on this project in time for it to be useful?