Question

prove that equation of motion by graphical metehod V²=U²+2as​

Answer 1

Explanation:

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Answer 2

$\huge{\underline{\tt{Question :-}}}$

Prove that equation of motion by graphical metehod V²=U²+2as​ .

$\huge{\underline{\tt{Solution :-}}}$

The distance travelled (s) by a body in time (t) is given by the area of OABC which is a trapezium.

In other words,

Distance travelled (s) = Area of trapezium OABC

s= (Sum of parallel sides) × Height/2

s = (OA + CB) × OC/2

Now, OA + CB = u + v and OC = t, putting these values in above relation,

we get; s = (u+v) × t/2 --------(1)

We now want to eliminate time (t) from the above equation. This can be done by obtaining the value of t from the first equation of motion.

Thus, v = u + at (first equation of motion)
and, at = v - u
so, t = (v-u)/a

Now, putting the value of t in the equation (1) above,

we get; s = (u+v) × (v-u)/2a

or, 2as = v^2 - u^2 [because, (v+u) × (v-u) = v^2 - u^2]

Therefore, v^2 = u^2 + 2as

{PROVED !}