Question

prove that newton- second is same as kilogram metre per second (kgms-1)

Answer 1

The DEFINITION in SI units is that
1 N is the force required to give a mass of 1 kg an acceleration of 1 m/s^2

i.e. 1N = 1kgm/s^2

This is a definition, not a proof.

Your equation is derived directly from this definition

Answer 2

thnxx :)