Question

Derive the equation for velocity-time relation (v = u + at) by graphical method.

Answer 1

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Answer 2

Answer:-

First, consider a body moving in a straight line with uniform acceleration. Then, let the initial velocity be u, acceleration be a, time period be t, velocity be v .

The initial velocity of the body, u = OA

The final velocity of the body, v = BC

From the graph,BC = BD + DC

So, 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 = at + u

or v = u + at

Hence Derived.

Explaination:-

The three equations of motion are :-

• v = u + at ;
• s = ut + (1/2) at2
• v2 = u2 + 2as