Question

Derive F = ma and state Newton's second law

Answer 1

✔️✔️Newton’s second law of motion states :-

⭕️The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.


⭕️the first one is done using differential process.

✔️✔️Newtons law uses :-

⭕️Using Newton's Second Law we can know how much force is acting on the car.

⭕️If the forces are unbalanced, the object will accelerate.

⭕️F=ma is very important because it shows the relationship between forces and motion.


⭕It allows you to calculate the acceleration.

Answer 2

$\huge\textbf{Newton's Second Law :}$

According to Newton's Second Law Force is directly proportional to the rate of change of linear momentum.

$\textbf{Mathematically}$

$\frac{dP}{dt}$ $\alpha$ $F$

$F$ $\alpha$ $\frac{dP}{dt}$

$F\:=\:K$ $\frac{dP}{dt}$

Now $P\:=\:mv$

So,

$F\:=\:K$ $\frac{d(mv)}{dt}$

$F\:=\:Km$ $\frac{d(v)}{dt}$

Now,

$\frac{dv}{dt}$ = $a$

So,

$F\:=\:K\:ma$

Experimentally K = 1

So,

$\textbf{F = ma}$

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