Question

Mathematical formulation of second law of motion.

Answer 1

The statement of Second Law states that," Rate of change of momentum is equal to the force and force is mass times acceleration."

Start with momentum,

Momentum(p)=Mass(m)*Velocity(v)

Change in Momentum=dp/dt=mdv/dt+vdm/dt; we generally work on constant mass systems, so mass remains constant and vdm/dt is ignored, reducing the equation to

dp/dt=mdv/dt; where, dv/dt is known as acceleration by your previous knowledge

dp/dt=m(a).

Hope this solves your problem.

The elaborated derivation for the illustrated text goes here

Answer 2

Answer:

The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalance d forces in the direction of force

Explanation:

the mathematical formulation of the second law of motion can be stated in the following way

change in momentum = p2-p1

mv-mu

m(v-u )

rate of change of momentum= m(v-u/t)

here a is acceleration which is the change in velocity

F = km(v-u/t)

here k is a constant of proportionality k =1

f=kma

f=ma