Mod Signs

[nbhindi]

Hey guys i'm just having difficulty identifying when you are able to remove the modulus signs for logs. I understand that you can't have the modulus of a -ve number, but i'm not sure how to go from:
t = 2loge[v-4]
t = 2loge(4-v)
Thanks

[jane1234]

You should remove the modulus signs if there is a restricted domain. In the example you gave, |v-4| = v-4 for v>=4 and 4-v for v<4.
So you'd take the modulus signs away and write loge(4-v) if the domain was v<4 or similar. 

[nbhindi]

The question was as follows: A body of mass 2kg in initially at rest and is acted on by a resultant force of v-4 newtons where v = velocity (m/s). The body moves in a straight line as a result of the force. Find v as a function of t.

How do you ascertain a restricted domain from this?

Thanks

[mpenman]

Ok spud.

R=ma
v-4=2a
a=(v-4)/2
dv/dt=(v-4)/2
dt/dv=2/(v-4)
t=-2loge[v-4]+c
t=-2loge(v-4)+c, v>4
t=0, v=0
0=-2loge(-4)+c
c=-loge(-4)
c=loge(-1/4)
therefore t=-2loge(v-4)+loge(-1/4)
t/-2=loge(v-4)+loge(16)
e^(t/-2)=v-4+16
therefore v=e^(t/-2)-12

YEAH BOI!!!!

I can guarantee I made a mistake probably 3rd line

[nbhindi]

WTF...After that completely flawed solution, a 30 for you is going to be equivalent (in terms of difficulty to attain) to a normal person getting 50. LOL 50 English and 40 Methods...BL SPUD.

Ok here's how to do it:

R = ma
v-4 = 2a
a = (v-4)/2
dv/dt = (v-4)/2
dt/dv = 2/(v-4)
t = 2loge[v-4]+c
t = 2loge(4-v)+c,  as v<0
t = 0, v=0 -----> .: c= -2loge(4)
t = 2loge((4-v)/4)
e^(t/2) = (4-v)/4
4e^(t/2) = 4-v
v = 4-4e^(t/2)
.: v = 4(1-e^(t/2))

 

[mpenman]

Oi how is v negative to make it (4-v)??
If v is greater than or equal to zero isn't it (v-4) instead of (4-v)?

[nbhindi]

But v is not greater than zero, from the question this is clearly ascertainable (in hindsight I look like a spud for asking this question...what was I thinking?). Failing to recognise this crucial part of the question lead you to have a -ve log in line 9 of your "solution" (note use of inverted commas) and as you may not be aware, you cannot have a -ve log. Dude no wonder you weren't able to make the cut for Dr He's epic maths class. 

[mpenman]

You sped. You asked the same question you gypsy. KJ wants in with noobs like that. 'Now wonder' god no wonder you're aiming for 38 for EngLang

[nbhindi]

come on i failed literature and want to get a 50 for english

[mpenman]

Yeah but I got 38 Biol - my Year 11 subject (the one you're meant to dominate) will be my 10&er. BL SON

[nbhindi]

dude stop making up ur scores for revs u got nothing over 36..at least i'm not that embarrassed to change my actual score just to fit in with the smart kids...wow this is turning out to be an epic mega troll

[mpenman]

Go to the Herald Sun you spastic and read my name. I would read yours, but oh wait, no 40 for you!!!

[Hutchoo]

Spam somewhere else plz <3

[mpenman]

Apologies

[nbhindi]

ultimate respect to Hutchoo the only person (aside from myself) who is actually sensible and trying to help