v=sqrt2gh and x=1/2atsqrd

[FutureDoc2]

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Hey guys I am having trouble seeing the relationship between variables in these equations. For ex. doubling v means h will be increased by 4 or doubling x, t will increase by 4. Is there an easier way to figure this out? Or should this be something I just memorize? Thanks!

 

[Erythropoietin]

Hey guys I am having trouble seeing the relationship between variables in these equations. For ex. doubling v means h will be increased by 4 or doubling x, t will increase by 4. Is there an easier way to figure this out? Or should this be something I just memorize? Thanks!

If you are having trouble with these, just plug in numbers.
For example v=sqrt2gh If you just want to increase h and keep g constant, then reduce the formula to v = sqrt 2h
2 is a constant so ignore that as well => v=sqrt(h)
Plug in 4 for h, you get 2 for v...so every time you increase height by 4, you double the velocity.

Do the same for x = 1/2at^2
If you want to see only the relationship between x and t, ignore everything else, so the equation now becomes: x = t^2
If you increase time by 2, x will increase by a factor of 4.

 

[FutureDoc2]

If you are having trouble with these, just plug in numbers.
For example v=sqrt2gh If you just want to increase h and keep g constant, then reduce the formula to v = sqrt 2h
2 is a constant so ignore that as well => v=sqrt(h)
Plug in 4 for h, you get 2 for v...so every time you increase height by 4, you double the velocity.

Do the same for x = 1/2at^2
If you want to see only the relationship between x and t, ignore everything else, so the equation now becomes: x = t^2
If you increase time by 2, x will increase by a factor of 4.

Thanks man, it now seems much easier when I do it this way. Does the same apply if one side of the equation with the variable in question is a fraction? For instance, P=nRT/V (PV=nRT) analyzing P and V... Thanks!

 

[Erythropoietin]

Thanks man, it now seems much easier when I do it this way. Does the same apply if one side of the equation with the variable in question is a fraction? For instance, P=nRT/V (PV=nRT) analyzing P and V... Thanks!

Yes, math is just numbers. Make sure you are holding everything else constant.. P=nRT/V ...So if you want to see the difference between P and V make sure n and T are not changing, (R is a constant anyway). If they are constant, the equation becomes P = 1/V
Since they are inversely proportional, when you double V, you reduce P by a factor of 2.
If you divide V by 2, then you increase P by 2.

I hope that answers your question