(i) By definition,
Acceleration=time takenchange in velocity⇒Acceleration=time takenfinal velocity - initial velocity
Hence,
a=tv−uat=v−u⇒v=u+at
Hence, we get,
v = u + at [Eq. 1]
(ii) By definition,
Distance travelled=Avg. Velocity×timeDistance travelled=(2Initial Vel.+Final Vel.)×time
or
S=(2u+v)×t
But, from Eq. 1, v = u + at
Therefore,
S=(2u + ( u +at))×tS=(22u + at)×t⇒S=ut+21at2
Hence, we get,
S = ut + 21 at2
(iii) By definition,
Distance travelled=Avg. Velocity×time⇒S=(2u+v)×t
But, from Eq. 1, v = u + at
or t = av−u
Therefore,
S=(2v+u)×(av−u)⇒S=2av2−u2
So, v2 - u2 = 2aS
Hence,
v2 = u2 + 2aS