Question

mathematical formulation of second law..????

Answer 1

Let a force F be applied on a body of mass m for time t due to which it's velocity changes from u to v.
Intial momentum=mu
Final momentum=mv
Change in momentum in t seconds
=mv-mu=m (v-u)
Rate of change in momentum
=Change in momentum÷time
=m (v-u)/time
but
acceleration a=v-u/t
Rate of change of momentum= m (v-u)/time
=mass ×acceleration
=ma