## how do you use kinetic energy and momentum to find speed?

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ohinsanity
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### how do you use kinetic energy and momentum to find speed?

but i am stuck on this physics problem and i think i might go crazy if i don't understand it.

if given that a moving object's kinetic energy and its momentum, how do you find its speed?

(a moving object has a kinetic energy of 123 J and a momentum of 36.9 kg*m/s. find the speed and mass of the object)

its totally killing me.

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Rgeminas
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### Re: how do you use kinetic energy and momentum to find speed?

Classically speaking, [imath]K=\frac{mv^2}{2}[/imath] and [imath]\mathbf{P}=m\mathbf{v}[/imath]. For your problem, [imath]mv^2=246[/imath] and [imath]mv=36.9[/imath]. Divide one equation by the other: [imath]\frac{mv^2}{mv}=\frac{246}{36,9}[/imath]. [imath]v=6.67 m/s[/imath].

ThinkerEmeritus
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### Re: how do you use kinetic energy and momentum to find speed?

Rgeminas gives the correct result, of course. BUT, you are going to see a lot of physics problems like this and even more complicated -- much more complicated. How do you approach them? You need a set of things to try when you get stuck.

Here is one very good set:

Find all the quantities and data mentioned in the problem. Here it is kinetic energy, momentum, mass, and velocity. The last two are to be determined, but they are quantities nevertheless.

Leaf through your mind, your notes, and/or your book for algebraic relations among the quantities. Especially don't forget definitions. Here you have KE in terms of mass and velocity, and momentum in terms of mass and velocity.

Are there enough relations to allow you to determine your unknowns? Here you have mass and velocity unknown, KE and momentum known, so two unknown quantities. You have two equations. Voila. If unknowns and relations hadn't matched, you would have to look for a relation you forgot to include or hope that one of the unknowns drops out. It is possible also that a relation may bring in another unknown quantity. If so, either you are going in the wrong direction or you should add that quantity to your list.

Figure out how to do the algebra.

On more complicated problems, it is best to find a check. One way is to plug all the knowns and now-determined values into your original relations (original meaning before doing the algebra) and make sure that the relations become identities.
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ohinsanity
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### Re: how do you use kinetic energy and momentum to find speed?

thank you both so much!
you both helped in different ways. [:
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z4lis
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### Re: how do you use kinetic energy and momentum to find speed?

I also sometimes write down equations that I feel might be relevant and place bars over the variables whose values I know. Then I can more easily look at unknowns in the various equations and try to figure out the best way to make some substitution. And if the algebra from such substitution on a particularly nasty problem becomes a too tedious to keep writing down over and over, just chug out a value and use it to far too many sig figs.
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VDOgamez
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### Re: how do you use kinetic energy and momentum to find speed?

<Smart aleck>Technically, you cannot find speed with those... You can only find velocity...</Smart aleck>

Mathmagic
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### Re: how do you use kinetic energy and momentum to find speed?

VDOgamez wrote:<Smart aleck>Technically, you cannot find speed with those... You can only find velocity...</Smart aleck>

What? Speed is just the magnitude of the velocity. If you have the velocity, then you have the speed.
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