Question

heya friends...

✓derive f=ma

Answer 1

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✨ Here's ur answer

Let us derive the relation of force F = ma from Newton’s second law:

According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.

It means that the linear momentum will change faster when a bigger force is applied.

Consider a body of mass ‘m’ moving with velocity v.

The linear momentum of a body is given by:

p = mv

Now According to Newton’s 2nd Law of Motion:

Force is directly proportional to rate of change of momnetum, that is

F α dp/dt

F = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

Experimentally k =1

F = k ma

Which is the required equation of force.

Answer 2

$Here \: is \: the \: answer \: of \: your \: question$


$\textbf{Newton's Second Law}$

According to it the rate of change of linear momentum of a body is directly proportional to the applied external force.
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$\textbf{Derivation}$

Force = (Change in momentum / Time)

Now, we know that;

Momentum = Product of mass and velocity of the body. i.e.

P = mv

Let us consider that a body of mass (m) is moving with a initial velocity (u) and with final velocity (v) in time (t)

Initial momentum = p1 = mu

Final momentum = p2 = mv

Then,

Change in momentum of the body = p2 - p1

F = mv -mu

F = [m (v - u) / t] .........(1)

As we know that,

a = [(v - u) / t] ...........(2)

Put the value of (2) in (1)

Then,

$\textbf{F = ma}$

which is Newton's Second Law

Hence, proved.
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