Question

Derive an expression on the newtons third equation of motion..... by graphically

Answer 1

Hello friend
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Thank you for your question...

Let's start.

The Newton's third equation of motion is the relation between Displacement and velocity.

See in above given figure !!!

We can determine the distance covered by the object time t from the area of the quadrangle DOEB.DOEB is a trapezium.So we can use the formula for its area .

s = area of trapezium DOEB

s = 1/2 x sum of lengths of parallel sides x distance between the parallel sides

s = 1/2 x (OD + BE ) x OE

but,OD = u,BE = v, and OE = t

hence,

s = 1/2 x (u + v ) x t ........(i )

But,a = ( v - u)/t

t = ( v- u)/a ..............( ii )


Now,

s = 1/2 x ( u + v ) x ( v - u)/a

s = (u + v) ( v - u)/2a

2as = (u + v) ( v - u) = v^2 - u^2

therefore,

v^2 = u^2 + 2as.


This is Newton's third equation of motion.


I hope this will helps you.

Thanks.