\$egingroup\$ No offence intended, but is momentum not simply simply an interpretation fairly than a derivation, it seems so intuitive to me, perhaps bereason I am provided to it. K.E., I guess was experimentally uncovered, not so sure around that derivation, did you look via history of math/nlinux.org? \$endgroup\$
You"ve gained it a little backwards - physicists first identified the quantity \$m cdot v\$ because it quantified the amount of "motion" a things possessed. They named it "momentum".

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Modern nlinux.org is generally pertained to through the amount \$m cdot v\$ (and also the updated versions of that quantity in even more recent framefunctions of nlinux.org) bereason it is conserved. This renders it exciting and helpful.

So, in short, tbelow is no derivation of \$p = m v\$, because it"s a definition. The quantity \$m cdot v\$ was offered a unique name of its very own bereason it is conserved, and also therefore necessary.

There"s an exciting roundup around the history of the concept of momentum on wikipedia.

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answered Aug 11 "15 at 23:29 BrioniusBrionius
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Jean Bouridan, rector of the College of Paris around 1350, was the first philosopher, to my knowledge, that specifically proclaimed the current principle of momentum. He sassist that impetus was proportional to the product of weight and rate.

Momentum is considered to be the product of mass and also velocity (velocity has direction as well as magnitude). Momentum is the tendency of a moving object to save relocating in the direction of its motion. It"s a conoffered amount, which means it can be moved from one object to one more, and it always requirements to be accounted for, as it can be neither created nor damaged within a device. For this reason, momentum is an extremely valuable idea in the evaluation of activity and also collisions.

An object of excellent mass relocating at excellent velocity is considerably more challenging to deflect or speak than a things of little bit mass relocating at low velocity. Momentum is straight proportional to mass and also velocity. That"s the intuitive knowledge of momentum.

Kinetic energy is the movement of a things. It"s measured in joules, one unit of which is the occupational done by one newton of force to move a things one meter in the direction of its activity. A joule is additionally referred to as a newton-meter when it is used to describe activity.

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The equation for kinetic energy is acquired from the work-related done by a force, which is acquired from Newton"s 2nd legislation of activity, F = m * a, where F is pressure, m is mass, and a is acceleration.

If work-related is done by a consistent pressure to relocate an object the distance s, Work = Fs = (ma)s. The distance s = average velocity * time. The acceleration a = (final velocity - initial velocity) / time. If you substitute these right into the equation for work-related, you get:

W = m * <(last velocity - initial velocity) / time)> * <1/2 (initial velocity + final velocity) * time>

W = 1/2 * m * (final velocity)^2 - 1/2 * m * (initial velocity)^2

Kinetic energy is identified as 1/2 * m * velocity^2. (The derivation is from Sermethod, nlinux.org, 1992)