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Kinematic equations

  1. Mar 21, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-3-21_23-25-15.png

    2. Relevant equations
    relevant equations are listed with each question

    3. The attempt at a solution

    25. **

    Displacement = 131 km (South)

    Average velocity = total displacement / total time

    Average velocity = 131 km (S) / 2.0 h

    Average velocity = 65.5 km /h (south)


    26. **

    Given information:

    v1 = 75 km/h

    Convert to m/s:

    (75 km/h) x (1000 m/1 km) x (1 h/3600 s) = 20.8 m/s

    d = 42 m

    total time = 3.4 s

    a)

    Calculate acceleration:

    a = v2 – v1 / total time

    a = 0 – 20.8 m/s / 3.4 s

    a = -6.12 m/s2

    Calculate distance:

    total distance= v1(total time) + ½ a (total time)^2

    = (20.8 m/s) x (3.4 s) – ½ (6.12 m/s2) x (3.4 s)2

    = 35.35 m

    Andrew travelled 35.35 m before stopping.


    b) ***

    Andrew did not hit the fox.

    42 m – 35.35 m = 6.65 m



    c) ***

    35.35 m / 4.2 m = 8.4 m

    It took approx. 8 van lengths for Andrew to stop.


    27. **

    Given information:

    v1 = 2.1 m/s (up)

    total time = 3.0 s

    acceleration = -9.81 m/s2 (down)

    a)

    Equation:

    total displacement = v1(total time) + ½ a (total time)^2

    Substitute and solve:

    d = (2.1 m/s) x (3.0 s) – ½ (9.8 m/s2) x (3.0 s)^2

    d = -37.8 = 37.8 m

    Marian’s Balcony is 37.8 m high.

    b)

    v2^2 = v1^2 + 2a(total displacement)

    = (2.1 m/s)2 + 2(-9.8 m/s2) x (-37.8 m)

    = √746

    = 27.3 m/s (down)










     

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    Last edited by a moderator: Mar 22, 2016
  2. jcsd
  3. Mar 21, 2016 #2

    haruspex

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    That's all about right, but you could have used a shorter and more accurate path in 27 a) and b).
    In a) do you know a SUVAT equation relating acceleration, time, initial speed and distance?
    In b) do you know a SUVAT equatiom relating initial speed, final speed, time and acceleration?
    (Using an intermediate result, as from 27a), as input to a further result often leads to loss of precision. E.g. while it might be appropriate to quote an intemediate result to 3 digits, you should use at least four as input to the next step.)
     
  4. Mar 21, 2016 #3
    can you explain what SUVAT equations are?
     
  5. Mar 21, 2016 #4

    haruspex

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  6. Mar 22, 2016 #5
    so for questions 25, and 26 are they completely correct?
    and when you say 'shorter and more accurate path to solve 27 a) and b)' do u mean that the answers are not as accurate as they should be? did i do it right or wrong?
     
  7. Mar 22, 2016 #6

    haruspex

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    They could be a bit more accurate. 27b is out by about 1 percent, whereas quoting three significant figures here implies about 0.3% or better.
    It's not a question of right or wrong. Using the best choice of equations from the SUVAT collection would have involved less working and produced more accurate answers.
     
  8. Mar 22, 2016 #7
    i see,
    what about 25 and 26, i feel like im missing something
     
  9. Mar 22, 2016 #8

    haruspex

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    Why? They look fine to me.
     
  10. Mar 22, 2016 #9
    ok thanks just clarifying :smile:
     
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