Question

explain newton'ssecond law in mathematically

Answer 1

Newton's Second Law of Motion.Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Mathematical Formulation of Second Law of Motion

Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.

Here we see that, the initial momentum

The final momentum

The change in momentum can be written as

As we know, the rate of change of momentum with respect to time is proportional to the applied force.

The applied force

Or,

as acceleration (a) = rate of change of velocity with respect to time.

where k = constant of proportionality.

The SI units of mass and acceleration are kg and m s-2 respectively.

So,

The second law of motion gives us a method to measure the force acting on an object as a product of mass of the object and the acceleration of the object which is the change in velocity with respect to time

Answer 2

Hey mate..✌

Here is your answer :-


NEWTON'S SECOND LAW :-
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Fα 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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