Write Newton’s second law of motion.

Explanation

Statement Time rate of change of momentum of a body is proportional to resultant force acting on it this change is in direction of resultant force .
Let resultant force `var(F )` act on body of mass for `Delta f` time interval During this let its velocity change from `vec(v ) ` to `+ Delta vec( v)`
Final momentum `p_(1) = m vec( v)`
`Delta p = p_(f ) - vec( p )_(1)`
`= mv + m Delta v - mv`
`= m Delta v`
From second law of motion
`vec( f) prop (delta vec(p))/( Delta t )`
by taking `underset (Delta to 9) (lim)`
`vec( F) = k (Delta p)/( Delta t )` where k is constant of proportionality
`vec( F) = k (d p)/( dt )`
`= km (dv )/( dt) + k vec( v) (dm )/( dt)`
` vec( F ) = km vec( a)`
` :. vec( F ) prop m vec( a)`
Thus force acting on body is proportional to product of mass and velocity
Definition of 1 N force : force which can produce acceleration of `1m//s^(2)` in body of mass 1 kg is called 1 n force
Definition of 1 dyne force : force which can produce acceleration of 1 cm `//s^(2)` body of mass 1kg called 1 dyne force