Velocity Integral problem

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jensgt

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May 2, 2011
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Hi everybody. I am in Calc 1 and having an issue with this problem. Here is the text.

The Velocity of a rabbit moving along a straight road going in an East/West direction is given by the equation Ds/Dt = V(t) = 4-2t meters per second. (Please sketch the function to assist you in the solution). The distance traveled by this rabbit, in meters, during the time interval 0 to 3 seconds is found to be:

A. 0
B. 5
C. 3
D. (Integral sign 3 to 0) (4-2t) dt

So I have made the sketch...its a straight line...and I figure this is one of the problems like we have had in homework where there are boxes with time vs velocity info....I have

0 1 2 3
__________
4 2 0 -2

So my issue is that in homework it has always stated to take the estimate from the left side or from the right side and here it does not specifically say. I am thinking East to West direction is a clue. Does that mean I should take the estimate from the right side...in which case it would be 0? Or from the left and then its 6...or if I go with the D answer and find the antidirivitive of 4-2t its 4x-t^2 and if I plug in 3 and 0 the answer I end up with is 3. 3 makes sense...but so does 0..when I am looking at the graph. So I am stuck. Could somebody please tell me which is the right answer and then explain why?

Thanks so much.
 
Distance travelled doesn't care if one is travelling forward or backward. It's all distance.

Try this:

∫03∣4−2t∣  dt\displaystyle \int_{0}^{3}|4-2t|\;dt

Don't you dare tell me you don't know how to deal with the aboslute values.

By the way, do not ever again find an antiderivative with respect to 't' and end up growing an 'x'. Very bad.
 
so C is the answer.

about the x's...I would not have done that on a test...just typing things in I screwed up.
 
Be that as it may, be more careful.

How did you deal with the absolute values?
 
The way I did the problem was 4t-t^2 So (4(3) - 3^2) - (4(0) - 0^2) Which = 3.
 
Ah, that would explain the incorrect answer! You can't just ignore the absolute values. Please try again.
 
Look no offense but you are coming off as super condescending. I had a test due Wednesday so I asked for help. I got a 94% on the test, but missed this question. Thanks for nothing.
 
And I do know what an absolute value is, but my teacher never used them while doing integration. I think I got stuck with a bad teacher. I have had to pretty much use the internet to teach myself.
 
No condescension, here. It is hoped that you might try and might learn. I am disappointed that you seem to have no desire to learn. Just a little effort might do it. 94% means very little compared to how much you might learn if you try to learn. If you try to memorize so you can reproduce problem types on an exam, this is of very little value in the real world. There isn't a problem-setup fairie out there dropping things on you so you can reproduce what you have seen before. Learning to THINK is the truly important part of the study of mathematics.

Use this principle and see if you can get it.

|x| = x if x >= 0
|x| = -x if x < 0
 
I don't see how you can assume that.

I am a 31 year old chemistry major with a 4.0 average. I am not a stupid lazy kid trying to cheat on my homework. I needed help, and asked for it in a specific way and you did not help me with that. I understand distance can not be negative and that is where absolute values may come in? I am TRYING to understand what you are saying, but I am not. I just had my husband, who is literally a rocket scientist, look at the problem and he is confused by it also. It is not always so easy to learn something new. If you understand it that is great but not everybody learns in exactly the same way. If you can not understand that, perhaps you are the one who needs to THINK.

FYI we just looked up this absolute value thing online in regards to distance and we figured it out. We did the integral separately from 0-2 and from 2-3 with absolute values and got the answer. I am relieved now that I understand and it was not that hard to understand!!!

I got an A on that test and could have easily been happy and moved on but as you see, I could not rest until I understood...so to say I don't want to learn...?? I learn by seeing how things are done. My teacher NEVER had shown us a problem like that, so it was new to me. I'm certainly no idiot, I just need things shown to me step by step when it comes to math and once I have it I have it.

So there is a lesson for you. I see you have many posts on this website. Good for you for helping so many people...but in the future please do not be so quick to assume the worst of people. We do not all work in the same ways.
 
I assumed nothing even remotely bad. Certainly not the "worst'. I dare you to point out where I inferred that you were lazy or cheating or an idiot.

jensgt said:
My teacher NEVER had shown us a problem like that, so it was new to me.
Click to expand...

This is the part I find the most interesting. This is the kind of problem that is most rewarding to solve. Anyone can solve the ones you've seen before.

Excellent work finding a method of solution. Not so excellent work failing to discover the answer in your own mind. You could have done it.

The idea that often is missed, when asking for help, is that the asker should trust the judgment of those from whom help is being sought. Rather than assuming that you know exactly what is needed, maybe accept honest, professional help that may not be quite what you expect. As far as your learning style, I'm afraid the method you describe does not allow for discovery, only memorization. I enjoy your strength and spirit. It reminds me quite strongly of soemone I met years ago. I was a young man of maybe 21 or 22. A woman in her 40s said to me, "When you get to be my age, you've learned your limits." It may have been the wisest thing I ever put into words to that point in my life. I looked her in the eye and said, "Or you've set them." Have you considered taking some strong personal direction and wandering into some intellectual discovery? You're far to young to be set in your ways as you have described.

Well, enough of that. Ready to learn some more mathematics? Let's see what you have.
 
"I am disappointed that you seem to have no desire to learn. Just a little effort might do it. 94% means very little compared to how much you might learn if you try to learn. If you try to memorize so you can reproduce problem types on an exam, this is of very little value in the real world. There isn't a problem-setup fairie out there dropping things on you so you can reproduce what you have seen before. Learning to THINK is the truly important part of the study of mathematics."

You don't see that as inferring that I was being lazy by not trying to think?

Memorizing to me means you are not understanding. I am not memorizing, I was only trying to understand. Now I understand. The way you tried to lead me I did not understand. That's all. You sound like an intelligent person but with a closed mind. There are different types of people...some learn by watching then doing. Nothing wrong with it as long as at the end you understand what you are doing and why you are doing it.

If you want to see what I have...I will let you know next Friday when my exam grades come in. I will be working my ass off for the next 6 days! :wink:
 
I spoke only of desire and how it seemed. Not a hint of "lazy" in there.

I will leave it with this:

1) It is a horrible question: How can I do that so I can get it right on the exam?
2) It is a good question: How can I do this?
3) It is a wonderful question: How can I discover how to learn this?

My impression of you.
1) Nowhere near this. Excellent.
2) You claim to be this. That is great.
3) There is so much more waiting for you.

Good luck.
 
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