CBSE Class 11-science Answered
can you tell me the newton second law of motion derivation
Asked by Viswanathan | 18 Sep, 2019, 11:27: PM
Expert Answer
Newton's second law states that rate of change of momentum of a body is directly proportional to the applied force and
takes place in the direction in which the force acts.
takes place in the direction in which the force acts.
Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv
i.e. its initial momentum p = m v changes by Δp = m Δv .
According to the Second Law, 
where k is a constant of proportionality.
Taking the limit Δt → 0, the term Δp/ΔT becomes differential co-efficient dp/dt of p with respect to t.
Thus F = k (dp/dt) ...............................(1)
if mass is not changing, we have dp/dt = m(dv/dt).
Also we have (dv/dt) = a, where a is acceleration of the body which is subjected to force F.
Hence Eqn.(1) becomes F = k m (dv/dt) = k m a ...................(2)
Let us choose units system as SI units and define 1 unit force as 1 Newton that produces acceleration 1 m/s2 on unit mass 1 kg.
Then k will become 1.
Finally, we write eqn.(2) in SI units as, F = m a
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