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Math Help - instaneous speed

  1. #1
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    I am in need of some serious homework help!

    A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function: s(t)=6t^3+72t^2.

    How many miles has the train traveled in 2 hour into the trip?

    What is the distance in miles from Columbia station to Penn Station?
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  2. #2
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    Quote Originally Posted by Hallah
    A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function: s(t)=6t^3+72t^2.

    How many miles has the train traveled in 2 hour into the trip?

    What is the distance in miles from Columbia station to Penn Station?
    Hello,

    sub in the given time into your equation:

    a) t = 2 h. Therefore s(2) = 6*2^3+72*2^2 = 336 miles

    b) The train needs 8 h for the complete travel. That means the distance between the two stations is s(8). Do as I've demonstrated in a). You should come up with 7680 miles. (Personal remark: I'm not very familiar with the geography of the United States, but this result looks as if the train zigzagged through all states on it's way from station to station)

    Greetings

    EB
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  3. #3
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    Quote Originally Posted by Hallah
    A high speed passenger test train ...
    Hello,

    here I am again. I've thought about the function given in your problem. This equation cann't be right.

    As I've said in my previous post, this very high speed train travels 7680 miles in 8 hours. That means it has an average speed of 960 miles per hour.

    In the air the speed of sound is 745 miles per hour. So this train travels faster than sound. Incredible!

    For example: If this train travels 10 hours, then the average speed is nearly twice as high as the speed of sound.

    So, please, check the text of your problem. There must be a (minor) mistake.

    Greetings

    EB
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  4. #4
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    Quote Originally Posted by earboth
    Hello,

    here I am again. I've thought about the function given in your problem. This equation cann't be right.

    As I've said in my previous post, this very high speed train travels 7680 miles in 8 hours. That means it has an average speed of 960 miles per hour.

    In the air the speed of sound is 745 miles per hour. So this train travels faster than sound. Incredible!

    For example: If this train travels 10 hours, then the average speed is nearly twice as high as the speed of sound.

    So, please, check the text of your problem. There must be a (minor) mistake.

    Greetings

    EB
    There probably is no mistake, just that whoever wrote the question didn't care about the physical nature of the distance function.

    -Dan
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  5. #5
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    Your Right this is an error. It should be a negative

    A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function:
    s(t)= - 6t^3+72t^2.

    How many miles has the train traveled in 2 hour into the trip?

    What is the distance in miles from Columbia station to Penn Station?
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  6. #6
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    Quote Originally Posted by Hallah_az
    A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function:
    s(t)= - 6t^3+72t^2.
    How many miles has the train traveled in 2 hour into the trip?
    What is the distance in miles from Columbia station to Penn Station?
    Hello,

    sub in the time t = 2 into your equation and you'll get:
    s(2)=-6*(2)^3+72*(2)^2 = 240 miles

    The complete journey takes 8 h. So plug in t = 8 into your equation to get the distance:
    s(8) = -6*(8^3)+72(8)^2 = 1536 miles

    By the way: This problem isn't much better than the first version because if the train travels 15 hours, it has travelled a distance of -4050 miles. That means it's going backward with a average speed of 270 miles / hour .

    Greetings

    EB
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