how to derive newtons second formula of motion

Asked by s.sreeram | 9th Dec, 2008, 06:35: PM

Expert Answer:

Newton's 2nd law of motion states that rate of change of momentum is directly proportional to the applied force and the change takes place in the direction of applied.

So accordingly, F = k dP / dt           (here, k is the constant of proportionality)

Now, if a body of mass 'm' moving with initial velocity 'u'  changes to final velocity 'v' in given time 't',

then, change in momentum ( dP ) = m ( v - u )

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

now following from definition, F = k dP / dt = m ( v - u ) / t

or,                                                 F  = K ma    [ (v-u)/ t = a ]

when m= 1 kg , a = 1 m/s2 and F = 1 N,   

     K = 1

so, F = ma    ; which is the formula or mathematical form of Newton's 2nd law of motion.

Answered by  | 9th Dec, 2008, 10:24: PM

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