Uniform Acceleration Motion (UAM)

  1. Hello I am new here. I came here because i was trying to search for a tutorial regarding Uniform acceleration motion or UAM but i am so unlucky since i havent found any decent ones that answers my questions.
    1. The problem statement, all variables and given/known data
    An automobile and a race car start from rest at the same instant, with the race car intially behind by 121m. The automobile has a constant acceleration of 2.00m/s^2, and the race car has an acceleration of 3.20m/s^2
    a) How much time does it take for the race car to overtake the automobile?
    b) Where does the car overtake the automobile?
    c) What is the speed of each when they are abreast?

    2. Relevant equations

    im sorry for this, i dont know how to put the subscripts and other small symbols :(
    v_{ave} = (v_i + v_f)/2
    v = v_0 + a t
    x = x_0 + v_0 t + (1/2) a t^2
    v[itex]^{}[/itex] = v[itex]_{}[/itex][itex]^{}[/itex] + 2 a \Delta x
    i dont know how to use the itex thing :( im sorry

    3. The attempt at a solution
    A) my solution for a is simply equating them using the forumla
    V=V0t + 1/2(a(t^2)) (i cancelled out V0t since the initial velocity is zero)
    but adding 121m to the side of the automobile since it is ahead
    so that would give me
    1/2(3.2)(t^2) = 1/2(2.0)(t^2)+121m
    1.6(t^2) = 1(t^2)+121m
    0.6(t^2) = 121m
    final answer is 14.2

    B) x=V0t + 1/2(3.20)((14.2)^2)
    again, i cancelled out V0t since the initial velocity is zero
    so my final answer is about 322.67m

    V^2=V0^2 + 2ad
    V^2 = 2(3.2m/s^2)(322m)
    V=Square root of 2060.8 m^2/s^2
    V=45.40 m/s

    V^2=V0^2 + 2ad
    V^2 = 2(2.00m/s^2)(322m)
    V=Square root of 1288 m^2/s^2
    V=45.40 m/s

    My major problem regarding this topic is i dont know WHEN to use WHAT equation.
    It really gives me a hard time thats why i resorted to this website in high hopes of finding great understanding. Hope you guys can help me :\ THANKS!
    Last edited: Jul 7, 2011
  2. jcsd
  3. Delphi51

    Delphi51 3,410
    Homework Helper

    Welcome to PF, xlrae.
    Part (a) looks great, though the V=V0t + 1/2(a(t^2)) was confusing. Should be d = Vot + 1/2at² of course. You can copy the ² and other symbols from this page: https://www.physicsforums.com/blog.php?b=346
    The trick to getting the right formulas is to write down your list of formulas and beside each, write what it is for. There are several formulas for constant accelerated motion, but you need the one giving distance as a function of time.

    I think you have a mistake in (b). Use either
    d = 1/2at² with the a=2 or d = 1/2at² - 121 with a = 3.2.

    I used V = Vi + a*t for (c) and got the same answer as you.
    Last edited: Jul 7, 2011
  4. wow thanks for the reply!
    actually, our teacher presented the answers and solutions to all the questions and i am right! thanks for the help!
  5. Delphi51

    Delphi51 3,410
    Homework Helper

    Most welcome. Good luck with the next set of problems.
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