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Acceleration problem

  1. Jul 23, 2014 #1
    1. The problem statement, all variables and given/known data

    a rocket is launched with constant acceleration for 16 secs and after 20 secs its reaches 5100m

    what is acceleration during first 16 secs
    what is velocity at 5100m

    2. Relevant equations

    v=v0+at

    3. The attempt at a solution

    I calculated the avg acceleration as 25.5 m/s^2
    I calculated the avg velocity as 255 m/s^2

    I know after 16 seconds the acceleration is -9.8 m/s^2

    i have tabulated various quants to try make sense of it and even did a position vs time graph but i can get further

    also did motion diagrams to show velocity vector and acceleration vectors
     
  2. jcsd
  3. Jul 23, 2014 #2
    Suppose you call the acceleration during the first 16 seconds "a". What is the velocity of the rocket at time zero (as it is being launched)? In terms of "a", what is its altitude after the first 16 seconds, and what is its velocity after the first 16 seconds?

    Chet
     
  4. Jul 23, 2014 #3

    Doc Al

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    Staff: Mentor

    How could you express (mathematically) the distance traveled during the first 16 seconds in terms of the unknown acceleration? (Call the acceleration "a".)

    How could you express (mathematically) the distance traveled during the next 4 seconds?

    What must they add up to?

    Edit: Chestermiller beat me to it!
     
  5. Jul 23, 2014 #4
    Velocity at start is zero and I don't have any values for at time 16s
     
  6. Jul 23, 2014 #5
    Ok thanks guys I have an idea now so will give it another stab in the morning

    Your help is much appreciated :) I managed the first 50 questions of this chapters exercise set but this one got me
     
  7. Jul 24, 2014 #6
    Hi guys

    If I use y1 = y0 + v0(t) + 1/2(a)(t)^2 then I get Y1=128a and Y2=8a

    so if i understand Doc Al correct then this should add up to 5100 meters so

    128a_1+8a_2=5100m

    a_1=(5100-8a_2)/128
     
  8. Jul 24, 2014 #7

    Nathanael

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    Homework Helper

    Why does Y2=8a?

    What's the velocity at the beginning of Y2? What's the acceleration?


    Edit:
    Try using a velocity vs time graph. That's actually an excellent way to solve the problem.
    (You'll need to know two basic "calculus" ideas: 1.) the slope of the velocity graph is the acceleration, and 2.) the area of the velocity graph is the distance. Since acceleration is constant, the slope is constant, meaning the graph is made of only straight lines.)

    If you don't immediately see the solution, then imagining the velocity vs time graph is certainly a great way to jump straight to the final equation.
     
    Last edited: Jul 24, 2014
  9. Jul 24, 2014 #8
    y1 = 128a
    v= 16a

    then

    y2=y1+v1(t)-1/2g(t)^2
    5100=128a+16a(4)-1/2(9.8)(4)^2
    5178=192a
    27m/s=a ?
     
  10. Jul 24, 2014 #9
    and

    Vf=Vi+a(t)
    Vf=16a+9.8(4)
    Vf=16(27)-9.8(4)
    Vf=392.8
     
  11. Jul 24, 2014 #10
    By trial and error on excel :
    Plug in :
    initial acceleration for 15 seconds @ 27.85 (m/s)/s
    Then decelerate under gravity for 5 seconds

    This should satisfy the results
     
  12. Jul 24, 2014 #11
    dont have excel in the exam :)
     
  13. Jul 24, 2014 #12

    Doc Al

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    Staff: Mentor

    Good! (Except the units should be m/s^2.)

    Good!
     
  14. Jul 25, 2014 #13
    Phase 1 : accelerating under power for 15 seconds.
    Phase 2 : decelerating unpowered for 5 seconds under gravity.

    If you get the answer by mathematical means, you will know if your procedure is correct (because you have the answer) saving you further work.
    You could post this enquiry on the mathematics section, you may get an improved response.
    By the way the velocity at 5100 m is 368.8 m/s exactly, and an improved answer for the acceleration is
    27.8533 (m/s)/s with the 3's recurring.

    Ive based these calcs on inputting an arbitrary value for (phase 1) acceleration, then calculating the distance and velocity after 15 seconds (when the motor shuts down), this velocity is then used for the slowing by gravity stage (lasting 5 seconds) as the initial velocity.
    Newtons equations of motion are used for both stages.
    I altered the value for initial acceleration value until the distance was correct ( (trial and error)
    The maths algorithm is beyond me, but it must exist or you wouldnt have been asked.
    Hope this helps
    Dean
     
  15. Jul 25, 2014 #14

    Doc Al

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    Staff: Mentor

    Those phases should be 16 and 4 seconds.

    There's no need for trial and error. The math is straightforward, as ryanbersa has demonstrated.
     
  16. Jul 26, 2014 #15
    oops, not reading the question properly, might as well use the algorithm again :
    revised solutions (16 and 4 seconds)
    acceleration = 26.9708333 (3's recurring)
    final velocity (g at - 9.8 (m/s)/s) = 392.333 (3's recurring)
     
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