Question

state Newton's second law of motion and derive it mathematically

Answer 1

Newton's 2nd law of motion:

The force applied on a body is equal to the product of the mass of the object and the acceleration of the body.

Derivation:

We know that the force applied on a body is directly proportional to the change in momentum.
$f \: \alpha \: \frac{mv - mu}{t} \\ f \alpha \: \frac{m(v - u)}{t}$
We know that (v-u)/t =a (acceleration)
So,
$f \: \alpha \: ma$
If we put an constant here,say,k then we can replace the sign of proportionality by the equal sign.And if take k=1,then we can remove the constant,k.

$f = ma$

Therefore,the force applied is equal ti the

Answer 2

Answer:

According to Newton's second law of motion, a body's force is inversely proportional to the rate at which its momentum is changing. When force "F" is applied to a body of mass "m," its velocity changes from u to v in time "t."

It is mathematically expressed as F = ma

Explanation:

1. The three fundamental laws of classical mechanics known as Newton's laws of motion describe how an object's motion and the forces acting on it interact.

2. According to Newton's second law of motion, a body's force is inversely proportional to the rate at which its momentum is changing. When force "F" is applied to a body of mass "m," its velocity changes from u to v in time "t." the second law of motion.

3. Mathematically, it can be expressed as,

F ∝ Change in momentum / Time

F ∝ (mv - mu) / t

Therefore, F ∝ m (v-u) / t

We know, (v - u) /t = a (acceleration)

Therefore, F ∝ ma

To remove proportionality, the constant is added

Therefore, F = kma where k = constant

∵ k = 1 (constant)

Therefore,

F = ma

where m = mass, a = acceleration and F = force

Thus, According to Newton's second law of motion, a body's force is inversely proportional to the rate at which its momentum is changing. When force "F" is applied to a body of mass "m," its velocity changes from u to v in time "t." It is mathematically derived as F = ma

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