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Math Help - Area Under A Graph

  1. #1
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    Area Under A Graph

    Given that the total distance travelled by a train is 4 km and the deceleration is 4 ms^{-2} for the first T second as shown in the speed-time graph below.Find:

    a)the value of T

    b)the value of V
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    The area under the curve represents that total distance traveled
    So

     \frac{(100-V)T}{2} + VT + VT + 2VT + \frac{(100-V)\cdot 2T}{2} = \color{red}{4000} ........(and not 4)

    And we are given deceleration so we get second equation

     100-4t= V

    Do you need more help?

    Adarsh
    Last edited by ADARSH; April 20th 2010 at 12:43 AM.
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  3. #3
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    Quote Originally Posted by ADARSH View Post
    The area under the curve represents that total distance travelled
    So

     \frac{(100-V)T}{2} + VT + VT + 2VT + \frac{(100-V)\cdot 2T}{2} = 4

    And we are given decelaration so we get second equation

     100-4t= V

    Do you need more help?

    Adarsh

    sir,why area of trapezium sir do like 1/2(100-v)T?not 1/2(100+v)T?ur anwer is correct sir..but i want to understand..
    Last edited by mastermin346; April 19th 2010 at 05:32 AM.
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    First of all its not a trapezium .. (to know more about trapezium try to search the word "trapezium" in Wikipedia/google)

    Ok here I will show you how I found that area

    1st step:

    Area of the two triangles (on the upper side) which will be formed when we form a line y= V

    they are found using the formula 1/2 x (base) x (height)

    Area of first triangle = 1/2 x (T) x (100-V)

    Area of second triangle = 1/2 x (2T) x (100-V)

    2nd Step :

    Area of that rectangle which is below the line Y= V

    = Length x Breadth

    Area of rectangle = V x 4T
    -------------------------------
    Add them you get the complete area

    as in previous post

    Feel free to ask if there is any other doubt.
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  5. #5
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    thanks very much sir..and when i get the coordinates (0,100) and (20,v)..i solve the question b that is to find the value of v..i find it gradient like 100-v/0-20=4 and i get v =180?? but the answer is 20ms^-2..can u help me sir?
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  6. #6
    Like a stone-audioslave ADARSH's Avatar
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    Use the second equation

    100-4xT = V


    This will give you the answer

    V = 100-4x20

    V =100-80 = 20


    _______________
    Sorry for my mistake in first post I should have been more careful.
    Its corrected in red.
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