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Normal and Tangential Acceleration

  1. Jan 29, 2013 #1
    1. The problem statement, all variables and given/known data

    A motorcyclist travels around a curved path that has a radius of 450 ft. While traveling around the curved path, the motorcyclist increases speed by 1.10[itex]\frac{ft}{s}[/itex]. Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.00 [itex]\frac{ft}{s^2}[/itex]

    2. Relevant equations

    a = √(at)2+(an)2

    at=[itex]\dot{v}[/itex]
    an = [itex]\frac{v^2}{ρ}[/itex]

    3. The attempt at a solution

    I've already solved for the speed at a given acceleration, and the magnitude of the acceleration at a given speed.

    But this part is a little confusing for me. I am thinking that I have to use the equation a = √(at)2+(an)2 and set a = 7.00 [itex]\frac{ft}{s^2}[/itex] and then I can solve for an.....then solve for v in the equation an = [itex]\frac{v^2}{ρ}[/itex], where ρ = 450 ft? But I'm not sure. I will give it a try, though.

    If anyone can weigh in on my approach, I would greatly appreciate it as always!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 29, 2013 #2

    Simon Bridge

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    That's how I'd interpret the problem - the total acceleration would be the vector sum of the tangential and centripetal accelerations.
     
  4. Jan 30, 2013 #3
    Thanks. Worked out fine.
     
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