Starting from F=ma, and using calculus, derive v=v₀+at and x=x₀+v₀ t+1/2 at^2.

See below.

Explanation:

Here using F = ma , we need to derive the fire and second equation of motion.

As we know that the rate of change of velocity is called acceleration. Therefore,

From equation (i) we have,

If the mass is constant,

On integrating both sides,

LHS will be integrated from v₀ to v and RHS will be integrated from 0 to t , as ;

Here a is constant , so ;

Adding v₀ both sides,

Hence we have derived the First equation of motion.

For second , as we know that ,

Integrating both sides, we have;

Putting the limits,

From first equation,

Distribute ,

Simplify,

Therefore we have derived the second equation of motion.

And we are done!

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

hope this ! this is not copied! search it up, it's free of plagiarism!