Question

12)Derive relation between velocity and displacement by graph method?

Answer 1

Answer:

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 = 1/2 × (sum of parallel sides + distance between parallel sides)

Distance(S)= 1/2 (DO+BE)×OE

S=1/2 (u+v)×t....(i)

a=v-u/t

from above equation we can say,

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

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

S=1/2a (u+v)(v−u)

2aS=(u+v)(v−u)

2aS=$v^{2} - u^{2}$

Hence Proved.

Explanation:

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