why don't these equal?

[deleted616051]

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If Vf=Vi+at and V=d/t then that means if the initial velocity is 0 then d/t=at => d=at^2.
This equation d=at^2 does not equal the kinematics equation d=1/2*at^2 when the initial velocity is 0. Why don't they equal?

 

[BerkReviewTeach]

V = d/t is an average velocity and you are plugging that value in for the final velocity. If you start at v=0 and finish at Vf, then Vavg is 1/2Vf. This means that Vf = 2Vavg, so you need to say that 2Vavg = at. That gives 2(d/t) = at which leads to d = 1/2at^2.

Whenever there is half in an equation that seems curious, it's usually the fact that it's an average value. That's where the 1/2 in PEspring = 1/2kx^2 comes from as well.

 

[deleted616051]

thanks. i also appreciate your quote...it's encouraging because i would like to do the same type of work one day.