Question

state newton second law of motion . Mathematically prove that F=ma , where symbol have usual meaning​

Answer 1

Newton's second law of motion describes the relationship between an object's mass and the amount of force needed to accelerate it. Newton's second law is often stated as F=ma, which means the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a). This means the more mass an object has, the more force you need to accelerate it. And the greater the force, the greater the object's acceleration.

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,

F =ma

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