Does anyone have the (algebraic)proof for initial velocity = final velocity during free fall?

Answer 1

Suppose u throw a stone with an initial velocity of V. Now it is going upwards. At top point its velocity is 0.

using v^2 - u^2 = 2as,

0 - V^2 = - 2gh
or h = V^2 / 2g

now the stone begins its downward fall from a height = V^2 / 2g
using
s = ut + 1/2 at^2

V^2 /2g = 0 + 1/2 g t^2

=>t^2 = V^2 / g^2
or t = V/g ;

Using v = u + at;

v = 0 + g (V/g)

final velocity before falling = V

hence proved

Answer 2

There´s no algebraic proof. See, when you drop something and let it fall freely it's initial velocity equals zero, since you dropped it from rest. At the end of the fall the object hits the ground and thus you can say that its final velocity equals zero too. In this case Vi = Vf.

But if you drop it with some initial speed then this is not true. I hope I got what you meant.

Answer 3

Initial velocity during a free fall is taken as zero..ie. u=0 and final velocity is taken as 9.8 m/s.

Answer 4

Hey.. you need to correct your question...
I think what you are asking is if something is thrown upward (neglecting effect of air)... the final velocity is equal to initial velocity....

Answer 5

Well, that would be impossible. Vo = 0, and Vf is determined by the height the free fall begins.

If h = 0, then Vo = Vf

Answer 6

well, i know that g=9.8 m/s^2 and the equation for g is
g=Vf-Vi/t

from there, you can turn that into:
Vf=(g)(t)+Vi
Vi=-(gt+Vf)
t=Vf-Vi/g

Answer 7

not sure what your asking

9.8 m/s/s