Question

Derive the equation for Newton's second law

Answer 1

Dear student,
Newton’s second law is a statement and not a Derivation. However we can derive the relation F =ma from Newton's second law.
This is given below.
Statement
Newton’s second law of motion states that: the net external force applied on an object is directly proportional to the rate of change of linear momentum of the object.

Let the external force be F, initial velocity be u ,final velocity be v, the time interval be t.

=> p1(initial momentum ) = mu

p2(final momentum )= mv

Therefore, (rate of change of momentum)

Δp=(mv-mu)/t

According to newton’s IInd law , F α Δp

=>F =k * (mv-mu)/t { k is a constant }

In S.I.Units, the value of k is 1

So. F= m(v-u)/t