You"ve acquired it a tiny backwards - physicists very first defined the quantity $m cdot v$ due to the fact that it quantified the amount of "motion" things possessed. They called it "momentum".
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Modern 6294.org is primarily concerned with the quantity $m cdot v$ (and the update versions that that quantity in an ext recent frameworks that 6294.org) because that is conserved. This renders it interesting and useful.
So, in short, there is no derivation of $p = m v$, since it"s a definition. The amount $m cdot v$ was given a one-of-a-kind name of its own due to the fact that it is conserved, and therefore important.
There"s an exciting roundup around the background of the concept of momentum on wikipedia.
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answered Aug 11 "15 in ~ 23:29
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Jean Bouridan, rector of the college of Paris around 1350, was the very first philosopher, to my knowledge, who specifically proclaimed the current concept of momentum. He claimed that motivation was proportional to the product that weight and also speed.
Momentum is thought about to it is in the product the mass and also velocity (velocity has actually direction and also magnitude). Momentum is the tendency of a relocating object come keep relocating in the direction that its movement. It"s a conserved quantity, which way it can be moved from one thing to another, and it constantly needs come be accounting for, together it can be neither developed nor ruined within a system. For this reason, inert is a an extremely useful principle in the analysis of motion and also collisions.
An thing of good mass relocating at an excellent velocity is substantially more difficult to deflect or prevent than an item of little mass relocating at low velocity. Momentum is straight proportional to mass and also velocity. That"s the intuitive knowledge of momentum.
Kinetic power is the activity of one object. It"s measure up in joules, one unit of i beg your pardon is the work done by one newton of force to move an item one meter in the direction the its motion. A joule is likewise called a newton-meter when it is provided to explain motion.
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The equation for kinetic power is acquired from the occupational done through a force, i beg your pardon is obtained from Newton"s 2nd law of motion, F = m * a, whereby F is force, m is mass, and a is acceleration.
If job-related is done by a continuous force come move things the distance s, Work = Fs = (ma)s. The distance s = average velocity * time. The acceleration a = (final velocity - early velocity) / time. If you substitute these into the equation because that work, friend get:
W = m * <(final velocity - initial velocity) / time)> * <1/2 (initial velocity + last velocity) * time>
W = 1/2 * m * (final velocity)^2 - 1/2 * m * (initial velocity)^2
Kinetic power is characterized as 1/2 * m * velocity^2. (The derivation is indigenous Serway, 6294.org, 1992)