Question

with the help of a diagram derive the position―time and velocity relations​

Answer 1

Explanation:

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 =21× (sum of parallel sides + distance between parallel sides)

Distance(S)=21(DO+BE)×OE

S=21(u+v)×t...............(i)

we know that,

a=tv−u 

from above equation we can say,

t=av−u...........(ii)

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

S=2a1(u+v)(v−u)

2aS=(u+v)(v−u)

2aS=v2−u2

Hence Proved.