SOLUTION: Why do we divide by 2 when solving problems involving gravity, 32 feet per second per second?

Question 370121: Why do we divide by 2 when solving problems involving gravity, 32 feet per second per second?
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Since acceleration is the derivative of velocity, when you integrate you get a term gravity linear in .
When you integrate velocity to get position, that linear term becomes a quadratuc term in the 1/2 is brought out during integration.
Hopefully that made sense to you.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
We don't always.
v = 32t
See?
----
To find the distance an object falls in, eg, 1 second, tho:
Its speed at the end of 1 second = 32 ft/sec, but its starting speed was zero.
That makes its average speed for that 1 second 16 ft/sec.
So, s = at^2/2 = 32*1^2/2 = 16 feet.
Or, s = 16t^2

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