inkyvoyd
  • inkyvoyd
Differential equations: Alison and Kevin are drag racing. They both travel with a constant acceleration. It takes Alison 3 seconds to complete the last 1/4 of the race. It takes Kevin 4 seconds to complete the last 1/3 of the race. Who won and by how much? I have the answers, but I want to know how to get them. Thanks.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
lgbasallote
  • lgbasallote
this is diff eq'n? sounds like it can be solved via physics.
inkyvoyd
  • inkyvoyd
Well, it can be solved by physics. But it's in my sister's diff eq text book...
inkyvoyd
  • inkyvoyd
@lgbasallote help you took the course don't run D:

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More answers

anonymous
  • anonymous
Let accleration =a then, velocity(v)= at+c
anonymous
  • anonymous
now, let total time taken By Alison to complete the race be x then |dw:1347849846129:dw|
inkyvoyd
  • inkyvoyd
Saura, I have to go to bed, but rest assured I will read this tomorrow. Thank you so much for helping out :D
anonymous
  • anonymous
|dw:1347850773445:dw|
anonymous
  • anonymous
Let y be the timetaken by KELVIN to complete the race.^
anonymous
  • anonymous
|dw:1347851115531:dw||dw:1347851153379:dw|
anonymous
  • anonymous
Solving i and ii....... we get: |dw:1347851218710:dw|
anonymous
  • anonymous
Thus, ALISON won the race by 1/2 seconds
inkyvoyd
  • inkyvoyd
Unfortunately, that's not what my book tells me...
inkyvoyd
  • inkyvoyd
@zepp
bahrom7893
  • bahrom7893
Alison and Kevin are drag racing. They both travel with a constant acceleration. It takes Alison 3 seconds to complete the last 1/4 of the race. It takes Kevin 4 seconds to complete the last 1/3 of the race. Who won and by how much? Okee, soo... If s(t) - distance travelled, then s''(t) = k
bahrom7893
  • bahrom7893
To get speed: v(t) = s'(t) = Int(k,t) = kt + C
inkyvoyd
  • inkyvoyd
Yessir. Then, we have \(\large s(t)=\frac{1}{2}at^2+v_0t+s(0)\)
bahrom7893
  • bahrom7893
You're right. I think we can just say s(0) as 0 because they're both travelling the same amount of distance. So we can just assume they both start at s=0 and end at s=s1
bahrom7893
  • bahrom7893
So s(t) = (V_i)t+(1/2)at^2
inkyvoyd
  • inkyvoyd
Start velocity is 0 as well.
inkyvoyd
  • inkyvoyd
but, start velocity for the last 1/4 and 1/3 of the race isn't 0.
bahrom7893
  • bahrom7893
It doesn't say that...
inkyvoyd
  • inkyvoyd
Nor, of course is starting distance.
bahrom7893
  • bahrom7893
oh drag racing
inkyvoyd
  • inkyvoyd
It doesn't say that, but I paraphrased te problem badly. It should be start velocity=0
bahrom7893
  • bahrom7893
So, s(t) = (1/2)at^2
inkyvoyd
  • inkyvoyd
yup
inkyvoyd
  • inkyvoyd
This is all I've gotten. I've drawn a picture and proved to myself that the problem is solvable, but i do want to solve it with diff eq and without a picture.
bahrom7893
  • bahrom7893
Wait I'm dumb, we're taking the somewhat wrong approach.. For Alison: d1 = (1/2)a*(t1)^2, v1 = a*(t1), d2 = (1/2)a*(t2)^2 + (v1)*(t2) + (d1), d1 = d2 - (d2/4), t = t1+t2, and t2=3
bahrom7893
  • bahrom7893
geezz that took a while to type out.
bahrom7893
  • bahrom7893
For Kevin: d1 = (1/2)a*(t1)^2, v1 = a*(t1), d2 = (1/2)a*(t2)^2 + (v1)*(t2) + (d1), d1 = d2 - (d2/3), t = t1+t2, and t2=4
inkyvoyd
  • inkyvoyd
Mmm
bahrom7893
  • bahrom7893
did you follow? distance 1 is the first part of the distance, and d2 is the whole distance.
inkyvoyd
  • inkyvoyd
Why are t2's 3 and 4? I mean t is total time, and t1 is elapsed time before that last part?
bahrom7893
  • bahrom7893
t1 is time before the last part of the distance for both, and t2 is the amount of time it took them for the last part. By the way for both sets t1s are not the same, and neither are t2s, I just didn't feel like writing out t11, t12 and t21, t22
bahrom7893
  • bahrom7893
now we just have ts to plugin and a few equations to solve, and this seems to be a pita, but, here goes: For Alison: d1 = (1/2)a*(t1)^2, v1 = a*(t1), d2 = (1/2)a*(t2)^2 + (v1)*(t2) + (d1), d1 = d2 - (d2/4), t = t1+t2, and t2=3 **** t = t1+3 d2 = (1/2)a*(3)^2 + (v1)*3 + (d1) = (9/2)a + 3(v1) + (d1) d2 = (9/2)a+3(v1)+(d2 - (d2/4)) 0 = (9/2)a + 3(v1) - (d2/4) (d2)/4 = (9/2)a + 3(v1) d2 = 18a + 12(v1) Now substitute: v1=a*(t1) d2 = 18a + a*(t1)
inkyvoyd
  • inkyvoyd
omg that's a lot of algebras.
bahrom7893
  • bahrom7893
For Kevin: d1 = (1/2)a*(t1)^2, v1 = a*(t1), d2 = (1/2)a*(t2)^2 + (v1)*(t2) + (d1), d1 = d2 - (d2/3), t = t1+t2, and t2=4 **** t = t1+4 d2 = (1/2)a*(4)^2 + (v1)*4 + (d1) d2 = 8a + 4(v1) + (d1) d2 = 8a + 4(v1) + (d2 - (d2/3)) 0 = 8a + 4(v1) - (d2/3) (d2)/3 = 8a + 4(v1) d2 = 24a + 12(v1) and plugging in v1=a*(t1) d2 = 24a + a*(t1)
bahrom7893
  • bahrom7893
hmm is there anything we didn't use yet? I'm assuming their accelerations are constant, but different, so t1s would also be different.. but d2s are the same.
bahrom7893
  • bahrom7893
man random messages are annoying me. New users are surprised to see a random level 99 pop up.. Hang on let me try this on paper and see what I get.
inkyvoyd
  • inkyvoyd
kk.
bahrom7893
  • bahrom7893
okay, I solved for the time it took Alison to complete the whole thing
bahrom7893
  • bahrom7893
actually I did something wrong.... YIKES!
inkyvoyd
  • inkyvoyd
oh no~!
bahrom7893
  • bahrom7893
Ok, I'm done working out this algebra... Just found this: http://www.chegg.com/homework-help/questions-and-answers/drivers-alison-kevin-participating-drag-race-beginning-standing-start-proceed-constant-acc-q303648 And no, you don't need a subscription to view that answer.
inkyvoyd
  • inkyvoyd
Loool. That was wonderful man. Don't worry, I'm not even enrolled in diff eq, so it doesn't really matter if I get full answers. (I'm in AP calc BC right now)
bahrom7893
  • bahrom7893
i miss ap cal bc, it was my fave class in hs :/
1 Attachment
inkyvoyd
  • inkyvoyd
man, I actually don't really get it, cause this guy won't use a carat. I'm sure I will tomorow though, when I'm less of a sleepy zombie. Thanks for the help man. I can finally move on to chap 2 of my sis' textbook. Btw, would you happen to have any good suggestions for a linear algebra textbook? I need to read up on linear if I hope to understand diff eq.
bahrom7893
  • bahrom7893
I'll pm you. The one I used was okay, but I suck at linear algebra.. it kinda seems that all I know is up to calculus 1-2
inkyvoyd
  • inkyvoyd
omg, I just copied the text, and all the subscripts and superscripts were there. :D
bahrom7893
  • bahrom7893
coool!
inkyvoyd
  • inkyvoyd
Wait, what was the name of the linear book o.o
bahrom7893
  • bahrom7893
http://www.amazon.com/Matrix-Analysis-Applied-Algebra-Solutions/dp/0898714540/ref=sr_1_15?ie=UTF8&qid=1348016409&sr=8-15&keywords=linear+algebra+and+its+applications I used this.
inkyvoyd
  • inkyvoyd
Thanks. I'll get a copy somehow.
bahrom7893
  • bahrom7893
I think there's a free pdf of it online. Just google it
inkyvoyd
  • inkyvoyd
Found it. Thanks so much man!
bahrom7893
  • bahrom7893
np

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