Consider an object of mass m moving along a straight line with an initial velocity *u *(say). It is uniformly accelerated to velocity *u *in time *t *by the application of a constant force *F *in time *t*.

Then, initial momentum of the object = *mu *

* P*_{1 }= *mu *

Final momentum of the object = *mv *

*P*_{2 }= *mv *

∴ Change in momentum = *mv *– *mu *= *m*(*v *– *u*)

The rate of change in momentum = {𝑚 \times (v−u) \over 𝑡}

According to Newton’s second law of motion, we have

𝐹 ∞ {𝑚(𝑣−𝑢) \over 𝑡}

𝐹 = 𝑘𝑚 {(𝑣−𝑢) \over 𝑡}

*F *= *k m a …….(1)*

Here, a = {𝑣−𝑢 \over t}= the rate of change of velocity.

= acceleration

* k *= a constant of proportionality

Putting m = 1 kg, a = 1 ms^{-2}

*F *becomes 1 N.

So, 1 N = *k *x 1 kg x 1 ms^{-2}

∴ *k *= 1

From equation (1), we have

*F *= *ma *

This represents the second law of motion.

Thus, the second law of motion gives a method to measure the force acting on an object as a product of its mass and acceleration.