# Relation between initial velocity, final velocity and acceleration

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.

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