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Math Help - instantaneous velocity

  1. #1
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    instantaneous velocity

    In a forward punch in karate, the fist begins at rest at the waist and is brought rapidly forward until the arm is fully extended. The speed v(t) of the fist is given in Figure 2-37 for someone skilled in karate. How far has the fist moved at (a) time t = 50 ms and (b) when the speed of the fist is maximum?
    Fig. 2-37
    Problem 68.




    I am not sure how to do any of this problem, please help me
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  2. #2
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    if you integrate velocity, you get distance, this must be well known in any calc class or calc based physics class

    since integration is a way to find the area under a curve, you must simply compute the area from 0 to 50

    for part b, you have a graph with velocity of the fist and you are looking for the maximum speed of the fist. Speed is the absolute value of velocity, but the velocity is never negative so speed=velocity in this case

    can you read the max velocity off of the graph?
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  3. #3
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    yes the max velocity is 7.5 m/s
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by BiGpO6790 View Post
    In a forward punch in karate, the fist begins at rest at the waist and is brought rapidly forward until the arm is fully extended. The speed v(t) of the fist is given in Figure 2-37 for someone skilled in karate. How far has the fist moved at (a) time t = 50 ms and (b) when the speed of the fist is maximum?
    Fig. 2-37
    Problem 68.




    I am not sure how to do any of this problem, please help me
    Broken link, upload image files to MHF rather than post a link. The linked images get lost and then the thread makes little sense.

    Ahh .. now it appears, but so it does not get lost here it is as an upload:

    instantaneous velocity-gash.png


    CB
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by BiGpO6790 View Post
    In a forward punch in karate, the fist begins at rest at the waist and is brought rapidly forward until the arm is fully extended. The speed v(t) of the fist is given in Figure 2-37 for someone skilled in karate. How far has the fist moved at (a) time t = 50 ms and (b) when the speed of the fist is maximum?
    Fig. 2-37
    Problem 68.




    I am not sure how to do any of this problem, please help me
    The curve from 0 to 50 seconds comprises two straight segments, and so its area is the sum of the areas a triangle and of a trapezium.

    The maximum occurs at 120 seconds and the area is the sum of the areas of the triangle from 0 to 10 seconds and the trapeziums from 10 to 50 seconds, from 50 to 90 seconds and from 90 to 120 seconds.

    CB
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