Derive the mathematical formulation of Newton's second law of motion F = ma.

Explanation

Let a force Fact on a body of mass m and change it velocity from u to v int second.
Initial momentum of the body `P_(1)` = mu
Final momentum of the body `P_(2)` = mv Change in momentum = `P_(2)-P_(1)`
mu-mu = m(v-u) Rate of change of momentum
=`("change in momentum")/("time taken")`
According to Newton.s second law of motion, the rate of change of momentum is directly proportional to the applied force.
`therefore ma prop F`
`therefore F=kma`
Where ,k is a constant of proportionality 1 unit force =`kxx(1kg)xx(1 ms^(-2))`.So the value of k becomes 1 .
`therefore=ma`