To convert acceleration from feet per second squared (ft/s^2) to feet per second (ft/s), you need to integrate the acceleration over time. In this case, if the acceleration is constant at 32.2 ft/s^2, the velocity can be found by multiplying the acceleration by time. Therefore, 32.2 ft/s^2 is equivalent to 32.2 ft/s.
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This is the standard expression for the ACCELERATION due to gravity.
Acceleration is the change in speed per second.
If there is no friction or air resistance then a body falling from rest will reach a speed of 32.2 fps after 1 second, after 2 secs it will be travelling at 64.4. fps, at 96.6 fps after 3 secs ....and so on.
In Mechanics there is an expression for motion involving constant acceleration :-
v = u + ft, where v = velocity after a period of time, u = initial velocity, f = acceleration and t = time.
In the question, after 3 seconds this formula would produce :-
v = 0 + 32.2 x 3 = 96.6 fps.
It cannot be proven because it is not true. Suppose S1 = {0,1,2,3} and S2 = {0,5,10} then S1 u S2 = {0,1,2,3,5,10} then |S1| = n = 4, |S2| = m = 3 but |S1 u S2| = 6 which is NOT n+m = 7
Area = square root of {s1(s1-a)(s1-b)(s1-p)} + square root of {s2(s2-c)(s2-d)(s2-p)} where a,b,c and d are the four sides of the quadrilateral, p is the diagonal separating the sides a,b from c,d, and s1 = (a+b+p)/2 and s2 = (c+d+p)/2
SxS = S2
p = 4s a = s2 2p = a - 48 8s = a - 48 8s = s2 - 48 -s2 + 8s + 48 = 0 s2 - 8s - 48 = 0 (s - 12)(s - 4) = 0 s = 12 or 4
A = s2 * 1.72