Question

derive an equation for second law of motion?

Answer 1

hey mate
here is your answer
 1. that the acceleration of an object of fixed mass is proportional to the force applied; and 2. that the acceleration on different objects created by a constant force is inversely proportional to the mass of the object.  The combined equation F = kma (where k is a constant) is how we usually state Newton's second law these days.  He stated it in a different, but equivalent, form. The "k" value is set to 1 in SI units as one newton is defined as the force required to accelerate 1kg at 1ms^-1. So we are left with the familiar F = ma.

Answer 2

is combining two experimental results, or assumptions if you like, mathematically: 1. that the acceleration of an object of fixed mass is proportional to the force applied; and 2. that the acceleration on different objects created by a constant force is inversely proportional to the mass of the object. The combined equation F = kma (where k is a constant) is how we usually state Newton's second law these days. He stated it in a different, but equivalent, form. The "k" value is set to 1 in SI units as one newton is defined as the force required to accelerate 1kg at 1ms^-1. So we are left with the familiar F = ma.