Question

prove 1st equation of motion

Answer 1

a = dv/dt
a.dt = dv
a (t-0) = v-u
at = v-u
v = u + at

Where v = final velocity
u = initial velocity

Answer 2

FIRST EQUATION OF MOTION
Vf = Vi + at


 Consider a body initial moving with velocity "Vi". After certain interval of time "t", its velocity becomes "Vf". Now

Change in velocity = Vf - Vi 
OR 
DV =Vf – Vi

Due to change in velocity, an acceleration "a" is produced in the body. Acceleration is given by

a = DV/t

 Putting the value of "DV"

a = (Vf – Vi)/t
at = Vf – Vi
at + Vi =Vf
OR
Vf = Vi + at. (proved)