Is the 2-independent group T test ok?

I would like a suggestion on what analysis to run for my data, and whether a 2-independent sample T test is ok to do because my dependent variable is additive. I have data on 2 independent groups, on a variable X collected at 4 time points. For simplicity, say that X is the number of words recalled during a task (it's actually more complicated than this but didn't want to get into the details). Say that the number of words was collected at 1 min, 2 min, 3 min, and 4 min and has to be represented in a continuous/additive fashion. I realize that with the variable being the number of words recalled, in theory you can say how many recalled in the first minute, second minute, third minute, and fourth minute, but for my more complex variable, I can't easily isolate the words from 0-1 minute, 1-2 minutes, 2-3 minutes, and 3-4 minutes. I have to collect it in a continuous/additive form, such that the results for number of words could be 7, 13, 17, 22 at the 1-4 minute time increments.

Since my dependent variable is continuous, although collected at 4 discrete points, I was wondering how this affected my analyses. I want to see at which time point(s) the groups differed. Can I just do four independent sample T tests between groups at 1 min, 2 min, 3 min, and 4 min? My 2 groups are independent (treatment and control group). I wonder if it is ok to do a T test because the result at 2 min is not actually entirely independent of my results at 1 minute, since the variable is continuous/additive.