Derivation between - Newton's first law,second law and third law.

 

Asked by kartikvns3 | 4th Apr, 2020, 10:25: AM

Expert Answer:

DERIVATIONS ARE AS FOLLOWS: - 

Newton's second law of motion states that the time of the rate of change of momentum is directly proportional to the resultant external force, and the change in momentum is in the direction of the resultant external force.

Mathematically, it states that the external force acting on a body is equal to the product of mass and acceleration of the body.

 

We know, 
Newton's second law of motion states that rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction in which the force acts. 
Thus, 
F o r c e space alpha fraction numerator C h a n g e space i n space m o m e n t u m over denominator T i m e space t a k e n space end fraction
T h u s comma space
F space equals space fraction numerator m left parenthesis v minus u right parenthesis over denominator t end fraction... left parenthesis 1 right parenthesis
 
Where, 
F - Force applied
m - mass
v - final velocity of an object 
u = initial velocity of an object
If there is no force acting on the body, the equation (1) can be written as, 
 
0 equals fraction numerator m left parenthesis v minus u right parenthesis over denominator t end fraction
T h u s comma space
0 space equals v minus u space  
 
→ v = u ... (2) 
 
This means initial velocity is equal to final velocity when no force acts on the body. 
 
Thus, equation (2) represents Newton's first law of motion. 
Newton's first law of motion states that a body at rest will remain at rest and body in motion will remain in motion in staright line with a uniform speed, unless an external force acts on it. 
 
In this way, we can derive Newton's first law of motion from Newton's second law of motion.

Answered by Shiwani Sawant | 4th Apr, 2020, 12:29: PM