Question

prove that F=ma(Force=mass.acceleration)

Answer 1

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 momentum, 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

#####Proved ####

Answer 2

$\huge\textbf{Law of Force :}$


It is Newton's Second law.

According to it the rate of change of linear momentum is directly proportional to the external force applied.

F α dp/dt 

F = k dp/dt

Now,

p (momentum) = mv

So,

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

(As, dv/dt = a)

Experimentally k =1

So,

$\textbf{F = ma}$

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