Question

Establish the relation v = u + at​

Answer 1

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acceleration = a

initial velocity = u

final velocity = v

time = t

`\sf t_1 = time \: of \: initial \: velocity \\ \sf t_2 = time \: of \: final \: velocity`

As we know

`\sf \red {a = (v - u)/(t_2 - t_1) }`

so further

`\sf a = (v - u)/(t) \\ \\ \sf at = v - u \\ \\ \sf v = u + at`

If we will make a velocity-time graph we will observe a linear curve

as shown in attachment

Answer 2

By definition of acceleration, we know that

Acceleration, a = Change in velocity / Time Taken

= (Final velocity – Initial velocity) / Time

= v-u/t

• at = v–u or v = u+at