Question

Show that newton's 1st law and third law are contained in 2nd la

Answer 1

The laws of motion are also called the laws of inertia. I call it laws of force (just for fun) also although I am probably the only person who calls it so. But let me tell you why I say what I say.
1st law: An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
This is an unnecessarily elaborate statement. It can be reduced to - An object remains in constant velocity unless acted upon by an unbalanced force.
Reason: After all, an object at rest has 0 km / h of constant velocity. So, no need to separately mention the object to be at rest as if it is a special case. If this argument is not enough then there is another argument i.e. the frame of reference. If you are moving at 100km / h and I am moving at 100 km / h in the same direction i.e. we both have constant velocities and same velocity, you would appear to me to be at rest.
Newton, having written a rather lengthy 1st law, decided to save some paper and made the 2nd law rather compact.
2nd law: F = ma.
It means that the unbalanced force is equal to the product of the mass of the body and the acceleration it undergoes.
Now, the relation between the 1st and the second law: The first law states - what happens when an unbalanced force is applied to a body. The second law states how it happens.
A way of connecting the two laws by an example would be. A billiard ball would rest on the billiard board unless an unbalanced force of a stick acts upon it and the measure of that force is the product of the mass of the billiard ball and the acceleration of the billiard ball.
Now, the bonus for asking a good question.
After writing an unnecessarily long 1st law and an extremely compact 2nd law, Newton took the middle way and finally wrote a mid-size final law.
3rd law: Every action has an equal and opposite reaction.
If you hit the billiard ball with a stick, the billiard ball also hits the stick back. That’s why the stick rocks back. It means that force applied by the stick to the ball is the same as the force applied by the ball to the stick, albeit in the opposite direction. It means mb.ab=ms.asmb.ab=ms.as. Again it is all about force.
This is why I also call the laws, rather mischievously, laws of force, without any disrespect to Sir Issac Newton.



Derivation of Newton’s third law of motion from Newton’s second law of motionConsider an isolated system of two bodies A & B mutually interacting with each other, provided there is no external force acting on the system.  Let FAB, be the force exerted on body B by body A and FBA be the force exerted by body B on A.  Suppose that due to these forces FAB and FBA, dp1/dt and dp2/dt be the rate of the change of momentum of these bodies respectively.  Then, FBA =  d p 1 dt     ---------- (i)       => FAB =   d p 2 dt     ---------- (ii) Adding equations (i) and (ii), we get,  FBA+ FAB =   d p 1 dt +   d p 2 dt   ⇒ FBA + FAB= d( p 1 + p 2 ) dt      If  no external force acts on the system, then  d( p 1 + p 2 ) dt      = 0 ⇒ FBA + FAB = 0 ⇒ FBA = - FAB---------- (iii)  the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction)...