Derive following equations for a uniformly accelerated motion where the symbols have their usual meanings: $v = u + a t$

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Solution

Consider a body of mass $m$ , having a initial velocity $u$ . After time $t$ , its velocity becomes $v$ due to uniform acceleration $a$ .
Since, $A c c e l e r a t i o n = \frac{F i n a l V e l o c i t y - I n i t i a l V e l o c i t y}{T i m e}$
Therefore, $a = \frac{v - u}{t}$
Hence, $v = u + a t$

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v^{2} = u^{2} + 2 a s

Derive following equations for a uniformly accelerated motion :

(i) v=u+at

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(iii) $v^{2} = u^{2} + 2 a S$

where the symbols have their usual meanings.

s = u t + \frac{1}{2} a t^{2}

Derive the following equation of motion by the graphical method :

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where the symbols have their usual meanings.

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