Derivation of the 1st equation of motion

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Solution

Consider a body of mass $m$ having a initial velocity $u$ .
Let after time $t$ , its final velocity be $v$ due to an uniform acceleration $a$ .

Now we know that:
$A c c e l e r a t i o n$ = $\frac{C h a n g e i n v e l o c i t y}{t i m e t a k e n}$

=> $A c c e l e r a t i o n$ = $\frac{F i n a l v e l o c i t y - I n i t i a l v e l o c i t y}{t i m e t a k e n}$

=> $a$ = $\frac{v - u}{t}$
=> $a t = v - u$

=> $v = u + a t$
This is the first equation of motion.

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