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Question

Derive an equation for position-velocity relation (2as=v2u2) by graphical method

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Solution

Let the initial velocity of the object = u

Let the object is moving with uniform acceleration, a.

Let object reaches at point B after time, t and its final velocity becomes, v

Draw a line parallel to x-axis DA from point, D from where object starts moving.

Draw another line BA from point B parallel to y-axis which meets at E at y-axis.

The distance covered by the object moving with uniform acceleration is given by the area of trapezium ABDO

Therefore,

Area of trapezium ABDOE =12× (sum of parallel sides + distance between parallel sides)

Distance(S)=12(DO+BE)×OE

S=12(u+v)×t...............(i)

we know that,

a=vut

from above equation we can say,

t=vua...........(ii)

After substituting the value of t from equation(ii) in equation (i)

S=12a(u+v)(vu)

2aS=(u+v)(vu)

2aS=v2u2

Hence Proved.










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