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Velocity and Acceleration Vector problem

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data
    A car moves on a circle of constant radius b. The speed of the car varies with time according to the equation, v = ct, where c is a positive constant.
    a) Draw a diagram showing the direction of the velocity and acceleration(s). Find the velocity and acceleration vectors (Directions of the vectors you have chosen to show in your diagram).
    b)Find the angle between the velocity vector and the acceleration vector. (Note: Express the angle in terms of c and t)


    2. Relevant equations
    V = dx/dt
    A = dv/dt


    3. The attempt at a solution
    Position Vector (from center of circle): b cos (u(t))i +b sin(u(t))j;
    u(t) = a function of time
    Velocity vector: -b u`cos(u(t))i + b u` sin(u(t))j;
    bu`(t) = ct
    u(t) = 1/2 (c/b)t^2

    Velocity Vector: -(c)(t)sin(1/2(c/b)t^2)i+(c)(t)cos(1/2(c/b)t^2)j
    Acceleration Vector: (c-(c^2 t^2)/b)cos(1/2(c/b)t^2)i+((-c^2 t^2)/b-c)sin(1/2(c/b)t^2)j

    I'm not sure if I did this correct. If not can you please show me my error and help with part b? :)
     
  2. jcsd
  3. Feb 11, 2014 #2

    haruspex

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    That differentiation is wrong - try it again.
     
  4. Feb 11, 2014 #3
    Thanks...
    Velocity vector: b u`sin(u(t))i - b u` cos(u(t))j;
     
  5. Feb 11, 2014 #4

    haruspex

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    You've corrected the trig functions but now the signs are wrong.
    For part (b), given two vectors, how do you find the angle between them?
     
  6. Feb 11, 2014 #5
    Oh yeah I forgot to put that didn't I? Cos (theta) = (v dot a)/(|v||a|) Is that correct?
     
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