Let us derive the relation between the initial velocity, final velocity and acceleration.
Suppose a body has an initial velocity u and is moving with uniform acceleration a.
Let the final velocity of the body after time t = v.
a = dv/dt
Or dv = adt …(i)
When‘t’ = o; velocity = u
When‘t’ = t; velocity = v
Integrating equation (i) between these limits, we have
∫dv = ∫adt
(a is uniform i.e. constant)
Or [v]vu = a[t]to
Or v – u = a (t – o) = at
Or v = u + at ….(ii)
This is the relation between velocity and acceleration. This is also the relation between initial velocity, final velocity and acceleration.