linear form equations

mawk

ok this might be badly explained but bear with me.

i need to rearrange a bunch of equations into linear forms so as to graph them and find out what the constants are.

when i say linjear form i mean they take the form y=mx+c

its ok if its something like T=kl^n cause i can log both sides and just split them but im too stupid to remember how to do it with something like

S=ut+1/2at^2 (where a and u are constant)

i guess i multiply both sides by 2 to get something like
2s=2ut+at^2 =
2s=t(2u+at) =
2s/t = 2u+at
y = c +mx


can i have a t on both sides?

and what about the form:
p=a/x +b ?

can that be logged using the logic log a/b =log a-log b
will that get me to linear form?

any help would be appreciated

breadmonkey

I don't understand. You are trying to express a quadratic function like s = ut + 0.5at^2 as a line?

breadmonkey

Actually, if you really want to, you can do it in Excel.

I can't upload the spreadsheet I used for some reason.

Graph s = ut +0.5at^2, then right click on the line and "add trendline", then select "linear", and then check the box beside "show equation on chart". This will give you some sort of line with its equation, though I somehow doubt this is what is required.

Delphi91

The easiest way to do that equation in physics is to plot a graph of S against t^2.

When t=0, the equation reverts to s = 0 + 1/2at^2, i.e. s = 1/2at^2.

This is in the form of y = mx + c with y = s and x = t^2.

That makes m = 1/2a.

So, plot the graph, calculate the slope and double it, to give a.


The best approach is to arrange the equation so that the term on the y-axis is the subject of the equation. Then factor out the x-term from the rest of the equation. The remaining terms will give the slope (m) and the intercept (c).


Mike

breadmonkey

When t=0, the equation reverts to s = 0 + 1/2at^2, i.e. s = 1/2at^2

I preume you meant when u=0?

I dont get this.

s = 1/2at^2 is not of the form y = mx +c, it is of the form
y = mx^2 + c and surely therefore cannot represent a line. What am I missing?

Smurfpiss

he's letting t^2 be the x axis. 1/2 and a are constants so yeah that is a line equation. though why its written like that i have no idea.
surely you could use the other two newtons equations to work out something nicer... like x vs t? v vs t?

mawk

i woulda loved something nicer and easier to work but thats what i was given to work with.

anywho i twigged it i think.

s=ut+.5at^2

so 2s=2ut+at^2

2s/t = 2u at

y = c + mx

like 2s/t is the y axis and t is the x


look right?

breadmonkey

I don't like dividing by t since it can be equal to zero.

Delphi91

Smurfpiss wrote:

he's letting t^2 be the x axis. 1/2 and a are constants so yeah that is a line equation. though why its written like that i have no idea.
surely you could use the other two newtons equations to work out something nicer... like x vs t? v vs t?

I used that equation 'cos it was the example given.

Its also the equation used in LC physics to measure the acceleration due to gravity, g when the method of freefall is used.

And yes, it was in the form of y=mx+c where y=s and x = t^2. That then gives m = 1/2(a). Since 1/2 is a contant, yoou can then work out a.

Mike