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]^v_u = a[t]^t_o

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.