Question

Derive
motion
mothematically the second law of
motion​

Answer 1

Answer:

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. Force applied is directly proportional to the product of mass and acceleration . ... We know that, Momentum ( P) = mv . Let v be the final and u be the initial velocity .

Answer 2

$\mathfrak{\underline{\blue{Statement:-}}}$

"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".

$\mathfrak{\underline{\red{Derivation:-}}}$

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

$\implies P_{1} = m×u$

The final momentum

$\implies P_{2} = m×v$

The change in momentum is :

$\implies \sf P_{2} - P_{1} = mv - mu = m(v-u)$

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

Then,

$\implies \sf \: f \: \alpha \: (m(v - u)) \div t$

And,

$\implies \sf F \alpha ma$

Since, acceleration (a) = rate of change of velocity with respect to time,

$\implies \sf \boxed{F = kma }$

Where,

• F is the force

• k is the constant of proportionality

• a is the acceleration

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

Therefore,

$\implies \sf \pink{\underline{\boxed{F = ma }}}$

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HOPE IT HELPS. :)