Physics Work question

Im just a little stumped here.
the question is:

The position of a 2 kg particle moving in the x-y plane varies as a function of time according to the expression r = [(6t+1)m]i + [(-5t^2 +8t +3)m]j

Find the work done on the particle between t=1s and t=5s.

So i evaluated r for r(5)-r(1) and came up with R = 24i - 88j
Now to me it looks as if the only force will be in the y direction as that is the only place there is acceleration. so i figured 2kg * -9.8m/s^2 = -19.6j N
So i did the dot product of 24i - 88j * 19.6j = 1724.8J
However the answer is 1760J and I can not account for the discrepancy.

Any help would be appreciated
--pete