How to derive equation for newtons second law of motion?

Newtonâ€™s second law of motion states that, â€śThe rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which force actsâ€ť.

Now, momentum is the product of mass and velocity.

Thus, change in momentum is

Thus, we have

But, is the acceleration of the body

Thus,

?

k is the constant of proportionality and in SI units, its value is 1.

F = ma

This is the equation of Newtonâ€™s second law of motion.

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