The force being exerted by the cord is m(a+g) if the bucket is being accelerated upward.
If T = 70 N, then a=70N/5.2kg−9.8m/s2=3.66m/s2is the maximum acceleration that it could have.
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Starting from rest, Δy = 1/2at2→ t = √2Δy/a = √2∗12.5/3.66 = 2.61s