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Math Help - A truck covers 80 m in 17 s while smoothly slowing

  1. #1
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    A truck covers 80 m in 17 s while smoothly slowing

    A truck covers 80 m in 17 s while smoothly slowing down to a final speed of 5.6 m/s
    a ) find its original speed
    b) Final its acceleration
    I want check my answer :
    a )
    Dx = 80 m
    t = 17 s
    v = 5.6 m/s
    v0= ??
    by appling the rule
    Dx = 1/2(v+v0)t
    80 = 1/2(5.6 + v0) 17
    v0 = .5 X 80 - 5.6 /17
    =2.023 m/s
    -------------
    b)
    v = v0 + at
    5.6 = 2.023 + 17a
    a = 5.6 -2.023/17 = 0.214
    plese help me and wha thw unit of a will be ?
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  2. #2
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    The average speed is 80 m / 17 s = 4.7 m/s. Since the final speed 5.6 m/s > 4.7 m/s, the truck could not have been slowing down; it must have been accelerating. To find the initial speed v0, use the fact that 4.7 is the average of v0 and 5.6, i.e., 4.7 = (v0 + 5.6) / 2.
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  3. #3
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    plese I want your help
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  4. #4
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    So, what is your difficulty?
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  5. #5
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    the diffculty I can't get v0
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  6. #6
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    I am using your equation Dx = 1/2(v+v0)t. Dividing both sides by t, we have that the average speed Dx / t is the arithmetic mean of the initial speed v0 and the final speed v = 5.6 m/s. This is how I got 4.7 = (v0 + 5.6) / 2. From here, 2 * 4.7 = 9.4 = v0 + 5.6, so v0 = 9.4 - 5.6 = 3.8 (approximately, since 80 / 17 = 4.7 only approximately).
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  7. #7
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    Hi plese I dont understand your answer clearly

    now I try to sovle this queation by another way anf please help me If it correct or not

    Dx = 1/2(v + v0)t
    80=1/2(5.6+v0) 17
    80 = 1/2(8.6 + 17v0)
    80 = 4.25 + 17v0
    v0 = 75.75/17 =4.45

    plese check my answer .
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  8. #8
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    Quote Originally Posted by r-soy View Post
    plese I want your help
    You were told by emakarov that initial velocity v0 is calculated from: 4.7 = (v0 + 5.6) / 2.
    SO:
    v0 + 5.6 = 9.4
    v0 = 3.8
    If that's not the answer, then your problem is not correctly stated.
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  9. #9
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    Dx = 1/2(v + v0)t
    80=1/2(5.6+v0) 17
    80 = 1/2(8.6 + 17v0)
    80 = 4.25 + 17v0
    v0 = 75.75/17 =4.45
    I don't understand how you got from the second line to the third and from the third to the fourth. For example, the third line should be

    80 = 1/2(95.2 + 17v0)

    By the way, the lack of attention that results in typos may well contribute to your mistakes in the solution.
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  10. #10
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    Quote Originally Posted by r-soy View Post
    Dx = 1/2(v + v0)t
    80=1/2(5.6+v0) 17
    80 = 1/2(8.6 + 17v0)
    80 = 1/2(5.6 + v0) 17
    Easier if you now went this way:
    160 = 17(5.6 + v0)
    160 = 95.2 + 17v0
    17v0 = 64.8
    v0 = 3.81176....

    80=1/2(5.6+v0) 17 really means: 80 = 17(5.6 + v0) / 2
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  11. #11
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    yes I want this way
    Easier to me
    160 = 17(5.6 + v0)
    160 = 95.2 + 17v0
    17v0 = 64.8
    v0 = 3.81176

    ny question why you multiply 80 X 2 ??
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  12. #12
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    If x/2 = 5, then x = 5 * 2
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