Question

derive the relation ( v^2 - u ^2 = 2 as ) by using graphical method

Answer 1

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 =

2

1

× (sum of parallel sides + distance between parallel sides)

Distance(S)=

2

1

(DO+BE)×OE

S=

2

1

(u+v)×t...............(i)

we know that,

a=

t

v−u

from above equation we can say,

t=

a

v−u

...........(ii)

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

S=

2a

1

(u+v)(v−u)

2aS=(u+v)(v−u)

2aS=v

2

−u

2

Hence Proved.