Question

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Derive v=u+at by graphical method.


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Answer 1

Answer:

The initial velocity of the body, u = OA

The final velocity of the body, v = BC

From the graph, we know that

BC = BD + DC

Therefore, v = BD + DC

v = BD + OA (since DC = OA)

Finally,

v = BD + u (since OA = u) (Equation 1)

Now, since the slope of a velocity-time graph is equal to acceleration a,

So,

a = slope of line AB

a = BD/AD

Since AD = AC = t, the above equation becomes:

BD = at (Equation 2)

Now, combining Equation 1 & 2, the following is obtained:

v = u + at

Step-by-step explanation:

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Answer 2

Derivation of v=u +at

Initial velocity u at A =OA

Velocity changes from A To B in time t(uniform acceleration a)

Final Velocity v=BC

BC=BD+DC

v=BD+Ao

v=BD+u

Slope of velocity time graph is equal to acceleration a.

BD=at.

Therefore v=u+at.

hence proved ..

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