newton law of motionsecond lawthe rate of change

Question

Newton law of motion:

Second Law

The rate of change of momentum is proportional to external force applied on the body and take place, in the same direction in which the force acts.

Let a body having mass 'm' is moving with a velocity 'u' along a straight line. It is acted upon some force 'F'

and the velocity of body becomes 'v' in time 't' then.

Initial momentum = m.u

Initial momentum = m.v

Change in momentum = m(v-u)

Rate of change of momentum = change of momentum / Time

= m(v-u)/t but         v = u + a.t

a = (v-u)/t

That is, Rate of change of momentum = m.a

But according to second law    F proportional to m.a

That is  F = k.m.a                Where K = constant.

Unit of force

1N = 1 kg-m/sec²  = 10⁵  dyne  = 1 grm.cm/sec²