Derive 1st law of motion from second law of motion

 

Asked by kukusabat | 17th Oct, 2019, 06:02: PM

Expert Answer:

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 | 18th Oct, 2019, 10:44: AM