Question

proove newton first law of motion with an example

Answer 1

As it’s already been pointed out, if you could prove it from a more fundamental principle, then you wouldn’t exactly have to call it a “law of motion” would you?

But I sense you’re actually touching on something deeper here. The question of why Newton chose to postulate such a law is very interesting. His first law is actually intimately connected to the principle of relativity, which he was very much aware of.

Consider the following alternative (and somewhat more intuitive) law of motion - “An object that’s at rest in some frame of reference stays at rest if no force acts on it.”

That’s it, no mention of constant velocity and all that other stuff. This is a perfectly reasonable and intuitive law of motion in a frame of reference that’s at rest with respect to said object. But this law must still obey the principle of relativity which implies that a second observer moving at a constant velocity relative to the first must also “discover” the same law.

But in the frame of the 2nd observer, the object is moving at a constant velocity in the opposite direction & the equivalence of the 2 observers implies that the trajectory of the object ought to be an undisturbed straight line (because any deviation would indicate the presence of a force which contradicts the observations of the first observer). Therefore for Newton’s first law to be compatible with the principle of relativity it must be extended to include the observations of the second observer as well and so naturally you get the law Newton presented in the principia.

What’s equally interesting though is that Newton was fully aware of the effect of gravitation. In fact he himself postulated gravity to be a force that acts on all objects in the universe uptil infinite distances. So the presence of gravity makes Newton’s first law completely useless in a universe with more than one particle (because every particle is always experiencing the force of gravity so the condition of no force acting is never realised). And I think we can all agree that there is atleast one more particle in the universe.

The modern interpretation of Newton’s first law gets around this problem by no longer perceiving gravity as a force. With the development of general relativity, Newton’s first law is modified to say - “An object, under the influence of no force, travels in a straight line through space-time.” So Newton’s first law actually becomes an experimental prescription for determining what a straight line is in the geometry of spacetime.

Answer 2

Newton's first law of motion states that an object at rest remains at rest and an object in motion remains in motion at a constant velocity unless acted upon by an unbalanced force. Velocity is the speed of an object in a specified direction. ... Newton's first law of motion applies to objects both on earth and in space.

Example:-
After staring the car engine, the car will move only then the driver gives the pressure on accelator. It means the driver gives the external force to the vehicle for movement. If the driver doesn’t give the external force, vehicle will be in the same position. It will not move.