Question

Mathematical formulation of second law..????

Answer 1

mathematical formula for Newton'second law of motion is: F-ma; that is force- mass * acceleration.

Answer 2

When a force 'F' acts on a body having mass 'm' , then it produces acceleration 'a' in the body in its direction and the acceleration produced is directly proportional to the force exerted and inversely proportional to the mass of the body. 

Mathematically; 
a α F -------------> directly proportional to Force 

a α 1/m --------> inversely proportional to mass 

Combining both, we get

a α F/m 
a = k.F/m --------> k is a constant and its value is taken as 1. 

a = 1. F/m 
a = F/m 
ma = F 
=> F = ma 
Force = Mass x Acceleration

Using this, we get

F = ma = Mass × Acceleration

Thus, we get Newton’s second law of motion