Question

derive the equation of motion that describes the relation between the position and the velocity of a body​

Answer 1

Answer:

answer is in imagery........

Answer 2

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)

we know that,

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 square - u square

Hence Proved.