Are you clear that v(t) is the derivative of s(t), and acceleration the derivative of that? If so, then your only problem is getting the derivatives right. For the first, can you see that the blank here will just be the bracketed expression involving k?
(set v(t) to zero and solve for t)
... and did you differentiate again?
(to show a(t) is constant)
Don't integrate - balloontegrate!
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