# How can I calculate the Newton's second law?

Apr 9, 2018

Newton's second law finds that $F = m a$

#### Explanation:

Newton's second law states that external force $F$ is directly proportional to the rate of change of momentum.

If initial velocity of an an object of mass $m$ is $u$ and after applying uniform force for $t$ seconds, its reaches a final velocity becomes $v$,

then its initial momentum is $m \times u = m u$ and final momentum is $m \times v = m v$ and hence change in momentum is

$m v - m u = m \left(v - u\right)$

and as it has taken $t$ seconds, rate of change of momentum is $\frac{m \left(v - u\right)}{t}$

But in case of uniform accelaration $a$, we have $v = u + a t$

or $\frac{v - u}{t} = a$ and then rate of change in momentum is $m a$,

hence $F \propto m a$

Now we can choose or define a unit of force that corrsponds to unit mass and unit accelaration and then we will have

$F = m a$