Question

Under what condition can we write $F=ma$?

Answer 1

According to Newton's second law of motion, the net external force acting on a body is equal to the rate of change of its momentum.
$F_{ext}=\frac{dP}{dt}$
We know taht, P = mv
$F_{ext}=\frac{d\left(mv\right)}{dt}$
If the mass (m) of the body is constant,
$F_{ext}=m\left(\frac{dv}{dt}\right)$
Now, $\frac{dv}{dt}=a$ [a is acceleration of the body]
$\Rightarrow F_{ext}=ma$