Question

Show that the first law of motion can be mathematically stated frm the mathematical expression for the second law of motion .

Answer 1

Derivation of Newton’s first law of motion from Newton’s second law of motion
 
Newton's first law states that a body stays at rest if it is at rest and moves with a constant velocity if already moving, until a net force is applied to it. In other words, the state of motion of a body changes only on application of a net non-zero force.
Newton's second law states that the net force applied on a body is equal to the rate of change in  its momentum. Mathematically,
 

 
Where, F is the net force, and p is the momentum. Now, we can write the same as:
 

 
So, if the net force, F is zero, change in the value of v is be zero i.e., a body at rest will be at rest and a body moving with constant velocity will continue with the same velocity, until a net force is applied. This conclusion is similar to the Newton’s first law of motion.
 
Thus, we can derive Newton’s first law of motion using Newton’s second law of motion.

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Answer 2

Answer:

Population growth is the increase in the number of individuals in a population. ... The global population has grown from 1 billion in 1800 to 7.8 billion in 2020. It is expected to keep growing, and estimates have put the total population at 8.6 billion by mid-2030, 9.8 billion by mid-2050 and 11.2 billion by 2100.

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