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2D kinematics question (2nd year of undergrad level.)

  1. Mar 30, 2015 #1
    1. The problem statement, all variables and given/known data
    An automotive test track forms a curve in the horizontal xy plane specified by y(x) =γx^3 / 2 where γ = 0.2 m^-1/2 and x ≥ 0 . A car moves along the track, starting at rest at the origin at time t = 0 , and picking up speed in accordance with v = ct , where c = 4.8 m s^-2 . The coefficient of friction between the car and the track is μ = 0.5 . At what position x does the car start to skid?

    2. Relevant equations
    (c^2+(v^2/R)^2)^1/2>=μg looking for x where this is true; when μg<=equation x will be the position at which it starts slipping.

    3. The attempt at a solution
    I know that v(x)=ct; therefore ds/dt=ct; (1+(y'(x))^2)^1/2 dx=ctdt; Can integrate and solve for t; which I can then plug into the above equation and have it only in terms of x which is what I need.
     
  2. jcsd
  3. Mar 31, 2015 #2

    BvU

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    Hello caj, welcome to the homework part of PF :smile: !

    Is there a question here ? You look all set and ready to go, so why not work it out ?
     
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