Question

first derivation of motion
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Answer 1

Graphical Derivation of First Equation of motion. Consider an object moving with a uniform velocity u in a strand line . Let it be given a uniform acceleration a at time t = 0 when its initial velocity is u .. The figure shows the velocity- time graph of the motion of the object.

Answer 2

Consider an object travelling in a straight path with initial velocity 'u' and uniform acceleration 'a'.Suppose it travels distance 's' in time 't'.

OA=CD=u

OE=BD=v

AC=OD=t

In ∆ABD

a = change in rate of velocity / time

a = BD/AC

a = BC - DC / AC

a = v - u / t.

at = v - u

$v = u + at \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: hence \: proved$

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