Question

Prove v=u+at graphically ​

Answer 1

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Answer 2

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✿ Deriving the first equation of motion [Velocity-time relation], graphically:-

v= u+at

As per the graph,

OA= u= initial velocity= DC

OE= v= final velocity= BC

OC= t= time taken

Now, let the velocity of the body changes at a uniform rate. So, acceleration of the body= a(say)

From the graph,

BC= B+DC

→BD= BC-DC

→BD= v-u (Consider it as the equation -1)

Now, acceleration from the graph can be calculated by the slope of the v-t graph..,and hence,

Acceleration, a= BC-DC/OC

→ a= BD/t

→a= v-u/t [From equation, 1]

→at= v-u [Change the sides]

→v-u =at [Take 'u' to the RHS and change the sign]

→ v= u+at [The first equation of motion..]

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