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Show that v=v(0)+at by graphical method....

Show that `v=v_(0)+at` by graphical method.

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A graph obtained by plotting velocity of a paricle along the Y - axis and time along the X - axis is known as velocity time graph.
Let at the initial time of observation, the velocity of the particle is `'v_(0)'` at A. Let 'v' be its final velocity at the end of t seconds at B.
The graph obtained is a straight line for an uniform accelerated motion of the particle. The slope of the line is given by `tan theta=(BC)/(AC)`

i.e. `tan theta=(v_(B)-v_(C))/(t-0)`
i.e., `tan theta=(v-v_(0))/(t)`
or `v-v_(0)=at`
`therefore" "v=v_(0)+at`
In vector notation, `vecv=vec(v_(0))+vecat`.
Note : For vertical motion `vecv=vecv_(0)-vecg t`.
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