Little difficulty, please help.

L

Lizzie

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Sep 8, 2005
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317
The problem:
The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.

The graph:
y axis is from 0 to 64 at intervals of 4 and is labeled v (for velocity)
x axis is from 0 to 6 at intervals of .4 and is labeled t (for time)
graphed line is straight and connects the points (0,64) and (6,0)

My difficulty:
How the heck do I do this? lol. I thought it was a simple thing, but either I got confused on something tiny or I just have no idea what I'm doing because What I ended up with was . . .

My answer:
d=192 units.

Any help would be greatly appreciated. Thanks!
 
Technically, "velocity" is the derivative of "position", so "position" (or, more specifically, the change in position) is the integral of "velocity".

Since this is a straight line, you can easily find the area between the line and the x-axis. (Either find the line equation and integrate, or just use geometric formulae.) This gives the change in position, otherwise known as "how far the car went before coming to a stop".

Eliz.
 
haha, yeah...*stares at her monitor with an idiotic look* I get it... uhm, lemme check what the heck that means and I'll get back to ya with what I get, lol. Thanks stapel! I appreciate your help! btw, I messaged you.
 
Lizzie said:
*stares at her monitor with an idiotic look* I get it...
Click to expand...
Don't feel bad. This is exactly why they give you these exercises: so you can start "seeing" the concepts and relationships. :D

Eliz.
 
lol, I finally found the section in my book where all this is explained, but now i have to understand... which i guess is the real problem.
 
...hmmm, it seems to me that what you're saying is to find the area between the graphed line and the x axis? In that case, what do I do with the area?
 
Hello, Lizzie!

The velocity graph of a braking car is shown.
Use it to <u>estimate</u> the distance traveled by the car while the brakes are applied.

The graph:
y axis is from 0 to 64 at intervals of 4 and is labeled v (for velocity)
x axis is from 0 to 6 at intervals of 0.4 and is labeled t (for time)
Graphed line is straight and connects the points (0,64) and (6,0)

My answer: d=192 units.
Click to expand...
Code: 
          |
        64*
          | \
          |   \
          |     \
          |       \
      - - + - - - - * -
          0         6
The distance is exactly the area under that graph (area of the triangle)
. . which you found.

From those intervals of width 0.4, I assume they want us to <u>approximate</u> the area
. . by dividing the region into 15 rectangles
. . and using left- or right-endpoints or midpoints.
 
OK, so I get as close to the area as possible and then that's the answer??

And I believe that I messaged you as well soroban.
 
Bleh, lol, the way I got my first answer was through a formula. But, I just found the approximate area by using 15 left endpoint rectangles and still got 192 as my answer...am I doing something wrong or is this the right answer?
 
No matter what I do, I keep coming up with 192... don't know what to do, I am so horribly stuck like an ant under a downfalling shoe with no where else to go but the afterlife...ok, so maybe I'm being a bit dramatic, but I am stuck, :).
 
Without seeing your steps, it's hard to say where you're going wrong, or even if you're going wrong. Note, however, that this is a nice neat straight line you're working with. If it had been a curvy line, you've have variable solution values, depending on the "error" introduced by the particular method you'd used. But nice straight lines can give (sometimes disturbingly) neat results.

Eliz.
 
Ok, here's exactly what I did. I made 15 left endpoint rectangles within the area. Then, I added all of their areas up. The areas that I had were as follows: 1.6, 3.2, 4.8, 6.4, 8, 9.6, 11.2, 12.8, 14.4, 16, 17.6, 19.2, 20.8, 22.4, and 24. When I added them all up, I got 192. That's all that I did.
 
I believe that I may be right because I just found a problem almost exactly the same and it was a multiple choice. All of the answers were between 100 and 150, and the graph was slightly smaller than the one I am working with now and they used midpoints, not left endpoints as I did. So their answers would be smaller. This means that it's quite possible for my answer of 192 ft to be correct! :) ! That would be good because then that means that I understood without too much help, just a few gentle nudges in the right direction...ok, maybe more than nudges.
 
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