Is a week long enough to write a 2500 word essay?Watch
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It probably mostly depends on your background for the topic and what reading you have (or haven't) already done for it. If you have to read a lot of primary and secondary literature before you can even start writing it might be a harder task, if you already have read the material and have a bibliography more or less laid out then you just need to actually write which is certainly possible.
Of course the longer you spend on TSR the less time you have for writing and researching