ICSE Class 9 Answered

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, 

 

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, 

 

  

 

→ 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.