The kinematic equations don't make intuitive sense to me…Why is VF+VI/2*t equivalent to 1/2(g)t^2?
Basically what I am asking is why is the average velocity multiplied by the time equivalent to saying 1/2 of g times the time squared? I'll give an example:
An object starting from rest goes through free fall. Assuming no air resistance, how far will it fall in 3 seconds?
Now I know the answer is 44.1 meters, that's not my question.
So you figure the initial velocity is 0m/s, and the final velocity is 9.8*3, which is 29.4 m/s.
29.4m/s+0m/s/2 *3s does equal 44.1 meters.
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However, 1/2(g)t^2 also works… 4.9*9 also equals 44.1 meters. Why is this? I wish I understood the mathematics behind this.
Can anyone explain? Thanks in advance.
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I try not to link to other websites but I think it would be clearer if you saw it written step by step by step and it would take me a long time to type it all out so here's a good site that takes every step to get from 1 to the other including your 2 (I went through and checked to make sure it did).
http://dev.physicslab.org/Document.aspx?doctype=3&...
I hope this quenches your curiosity.
Yours is equation 5 but they use equation 2 and 3 to prove equation 5 so it's best to look at the equations before 5