Question

What is the Newton's second law of motion?
Give the derivation_?​

Answer 1

$\textbf{\large{\underline{ \underline{Newton's Second law of Motion} }}}$

According to Newton's Second law — Applied force is directly proportional to the rate of change of the momentum of the body and takes place in the direction in which the force acts.

$\text{\large{\underline{ \underline{Derivation :</strong><strong>-</strong><strong>} }}}$

$\text{Force} \propto \: \frac{ \text{Change in momentum }}{ \text{ Time taken}}$

$\: \: \: \text{F} \propto \frac{ \text{mv - mu}}{ \text{t}} \\ \\ \: \: \: \text{F} \propto \frac{ \text{m(v - u)}}{ \text{t}} \\ \\ \textsf{we \:know \: that : - } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ \text{(v - u)}}{ \text{t}} \text{ = a} \textsf{ \small{(acceleration)}} \\ \\ \text{F} \propto \text{m} \times { \text{a}}$

$\text{ \small{Turning the relation of }} \text{F} \propto \text{m}\times {\text{a}} \\ \text{ \small{into equation by putting a constant }}{ \textbf{k}}$

$\textsf{F = k \times m \times a}$

The value of Constant k in SI unit is 1.

Since, the above equation becomes —

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\textsf{ \: \: F = m \times a \: \: }}$

$\textbf{Force = mass \times acceleration}$

Answer 2

Answer:

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.

For derivation see attatachemt...

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