Question

Explain the mathematical derivation of 2nd law of motion .
f=kma​

Answer 1

Answer:

Derivation of equation f= kma

Let a body of mass m be moving with an initial velocity u . if an external force f is applied on it then it's final velocity v after time

Now

initial momentum of body p1 =mu

final momentum of body p2 = mv

change in momentum of body = p2 _p1

= mv -mu

= m(v-u)

Rate of change of linear momentum

$= \frac{m(v - u)}{t}$

we know that ,

$\frac{v - u}{t} = a$

we know that rate of change of momentum of body = ma

from Newton second law of motion

Rate of change of linear momentum= applied force (f)

so FORCE = MASS *ACCELERATION

F= ma

Hence proved

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