Hmmm the object, is at rest, when dropped, so it has a velocity of 0 ft/s
the only force acting on the object, is gravity, using feet will then be -32ft/s²,
was wondering myself on -32 or 32.. but anyhow... we'll settle for the negative value, since it seems to be just a bit of convention issues
so, we'll do the integral to get v(t) then

when will it reach the ground level? let's set s(t) = 0

part B) check the picture below
Answer: 14x^7
You add the coefficients (numbers to the left of the variable terms) to get 6+8 = 14 which is the coefficient of the final answer. The x^7 stays the same. It's like saying "we have 6 apples added to 8 apples, so there are 14 apples overall". Replace "apples" with "x^7" and it's the same idea.