Question

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

Answer 1

Answer: V = u + at

Explanation:

The equation for velocity-time relation (v=u+at) by graphical method,

Let the initial velocity for a body be u = OA = CD

Now, the final velocity of a body is V = OE = CB,

Time (t) = OC = AD

Now BC = CD + BD

BC = BD + AO

V = BD + U

BD = V - U

In velocity, time graph slope gives acceleration,

$a = \frac{BD}{AD} = \frac{BD}{OC}$

OC = t,

a = $\frac{BD}{t}$

Now, BD = at

So now substitute equation 2 in 1, We get

BD = v - u

at = v- u

So now, V = u + at

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Answer 2

Explanation:

Velocity is given by OA= CD= u

Final velocity given by OE= BC= V

Time is given by OC= AD= t

BC= BC + CD

V= BD + OA

V= BD + u

BD= V - u

From the graph we know a= BD/AD

a= BD/E

BD= at - 2

Substituting 1 and 2 we get at

at = v - u

at + u = v

v = u + at