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I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

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13  
Integrate acceleration twice wrt time. – jinawee Dec 9 '13 at 11:51
up vote 53 down vote accepted

It is exactly because we have a factor of $\frac 1 2$ in the area formula of a triangle. To understand what I'm saying, consider what is the $v(t)$ graph of a particle under constant acceleration.

enter image description here

Some say, a good plot is worth a million words! :)

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+1: Great and simple to comprehend answer. – user29727 Dec 9 '13 at 13:05
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The positive reaction to this answer is way better than what I was expecting! Thanks to everyone. – Ali Dec 9 '13 at 17:54
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@Ali Part of it I think is that clarity in technical writing is a jewel to behold. – WetSavannaAnimal aka Rod Vance Dec 10 '13 at 13:36

We can also do it using calculus,the displacement of the particle is given by enter image description here

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protected by Qmechanic Dec 17 '13 at 9:04

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