what is kinematic some formula of integration
∫a∫a dt=vdt=v
∫v∫v dt=sdt=s
where aa = acceleration, vv = velocity, and ss = displacement
Beginning with the first integral:
∫a∫a dtdt
=at+c=at+c
=v=v
v=c+atv=c+at
Here, cc represents some arbitrary constant. When it comes to motion, cc would represent the initial velocity of the moving body. Commonly, that is represented as uu, so I’m going to change it to
v=u+atv=u+at
Now the second integral:
∫v∫v dtdt
=∫u+at=∫u+at dtdt
=ut+12at2=ut+12at2
=s=s
So,
s=ut+12at2s=ut+12at2
These are some of the equations of motion that can be derived using integration. Of course, there are other equations of motions that I haven’t mentioned, like
v2=u2+2asv2=u2+2as
and
s=(v+u)t2s=(v+u)t2
