Question

derive the mathematical equation for Newton's second law​

Answer 1

The BIG Equation. Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Answer 2

$\huge\red{HELLO\:MATE}$

$<b>The second law of Newton states that the rate of change of momentum is directly proportional to the applied force in the direction of the force.</b>$

So,

(Here we have taken ♂ as the sign of proportionality)

p2 - p1 ♂ F

or mv2 - mv1/t ♂ F

or m( v2 - v1 )/ t ♂F

or m (v2 - v1 )/t ♂ F

or m × a ♂ F.

or m × a × k = F.( where k is constant)

Therefore:$<b> F = m × a</b>$