Question

State newtons 2nd law of motion and show that the first law of motion can be mathematically stated from the mathematical expression for the second law of motion

Answer 1

Newton's second law states that the net force applied on a body is equal to the rate of change in  its momentum.

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

The second law of motion states that the rate of change of momentums of an object is proportional to the applied unbalanced force in the direction of force

The first law of motion can be mathematically stated from the mathematical expression for the second law of motion. Eq is

F=ma

or F= m(v-u) / t

or F= mv-mu

That is, when F=0,v=u for whatever time t is taken. This means that the object will continue moving with uniform velocity, u is throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest

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