(i) What is the Newotons second law of motion write its mathematical expression and its application? (ii)derive Newtons first law from second law expression
Answers
Explanation:
1.Newton’s second law of motion is closely related to Newton’s first law of motion. It mathematically states the cause and effect relationship between force and changes in motion. Newton’s second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force. Before we can write down Newton’s second law as a simple equation giving the exact relationship of force, mass, and acceleration, we need to sharpen some ideas that have already been mentioned.
First, what do we mean by a change in motion? The answer is that a change in motion is equivalent to a change in velocity. A change in velocity means, by definition, that there is an acceleration. Newton’s first law says that a net external force causes a change in motion; thus, we see that a net external force causes acceleration.
Another question immediately arises. What do we mean by an external force? An intuitive notion of external is correct—an external force acts from outside the system of interest. For example, in Figure 1(a) the system of interest is the wagon plus the child in it. The two forces exerted by the other children are external forces. An internal force acts between elements of the system. Again looking at Figure 1(a), the force the child in the wagon exerts to hang onto the wagon is an internal force between elements of the system of interest. Only external forces affect the motion of a system, according to Newton’s first law. (The internal forces actually cancel, as we shall see in the next section.) You must define the boundaries of the system before you can determine which forces are external. Sometimes the system is obvious, whereas other times identifying the boundaries of a system is more subtle. The concept of a system is fundamental to many areas of physics, as is the correct application of Newton’s laws. This concept will be revisited many times on our journey through physics.
2.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,

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