Question

how can the first law of motion be mathematically expressed using second law of motion​

Answer 1

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.

Answer 2

Hey mate..

Newton's first law states that a body stays at rest if it is at rest and moves with a constant velocity unit if a net force is applied on it. Newton's second law states that the net force applied on the body is equal to the rate of change in its momentum. That is, when F = 0, v = u for whatever time, t is taken.

I hope it's helpful...

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