Question

Mathematical formulation of newtons second law of motion

Answer 1

Explanation:

suppose an object of mass ,m is moving along a straight line with an initial velocity,u. it is uniformly accelerated to velocity v in time, t by the application of a constant force,F throughout the time,t.

The intial and final momentum of the object will be

$p1 = mu \: and \: p2 = mv$

respectively.

The change in momentum is directly proportional to

$p2 - p1$

$mv - mu$

$m \times (v - u)$

The rate of change of momentum is directly proportional to

$m \times ( v - u) \div t$

or the applied force, F is directly proportional to

$m \times (v - u) \div t$

or the applied force,

$f = km \times ( v - u) \div t$

$= kma$

partially solved