Question

please someone help me to derive all 3 equations of motions with graph

Answer 1

I)1st equation
OA=CD=u
BC=EO=v
OC=AD=t
slope AB=a
a=change in velocity/time
a=BC-CD/AD
a=v-u/t
at=v-u (or)v=u+at
a=BD/t
BD=at
t=v-u/a
II)2nd equation of motion
Area of the graph(shaded area)=dispacement of the moving object
s=area of rectangle+area of triangle
  =OADC+ABD
s=lxb+1/2bh
  =ADxOA+1/2ADXBD
  =t x u +1/2 x t x at
  =ut+1/2at2
(s=displacement)
III)3rd equation
position velocity

Area of trpezium=1/2h(a+b)
                       s  =1/2 AD(OA+BC)
                           =1/2 t(u+v)
                           =1/2 x(v-u)(v-u)/a
                           = v2-u2/2a
                     2as=v2-u2