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Find Acceleration using Velocity and a given equation

  1. Jan 25, 2013 #1
    1. The problem statement, all variables and given/known data

    A race car starts from rest and travels east along a straight and level track. For the first 5.0s of the car's motion, the eastward component of the car's velocity is given by vx (t) = (0.920m/s^3) t^2.

    What is the acceleration of the car when vx = 13.9m/s ?

    2. Relevant equations
    a= Δv/Δt


    3. The attempt at a solution
    I attempted to solve the problem by using the given formula for vx(t)
    13.9 = (.92m/s^3)* t^2

    With this i solved for t and got 3.89s. so using this I put it in to the formula for a

    (13.9 - .92)/(3.89-1) = 4.5m/s

    Unfortunantly this was wrong. can anyone help me? Should I have subtracted 0 for both initial velocity and initial time? or was that general thought process right?

    Thank you.
     
  2. jcsd
  3. Jan 25, 2013 #2
    I am unsure as to if you have learned how to do derivatives yet. But that is the easiest way of solving this. The derivative of displacement is velocity, and the derivative of velocity is acceleration. Have you by any chance learned derivatives yet?

    I will explain using the derivative.
    First thing you need to do is find the time when the speed is 13.9 m/s.
    Fill it into the equation and isolate t as you did. I also got 3.89 s.

    Next is getting the acceleration equation. Take the velocity equation.
    V(x)=0.920t^2
    The corresponding acceleration equation for this is in the form
    a(x)= (Exp)(base numer)(t)^(exponent - 1)
    a(x)=1.840t

    Now input the time into the equation and you should get your answer.
     
    Last edited: Jan 25, 2013
  4. Jan 25, 2013 #3
    Thank you for the help. Using the derivative I was able to get it right. Unforunatnly I have no yet learned how to do them. My professor spoke of them being used here, and I was intending on learning them on my own.

    So I'm assuming I should learn how to do derivatives and integral as soon as possible to be able to do most if not all of my next homework problems.

    But thank you for the help!
     
  5. Jan 26, 2013 #4
    No problem. Happy to help. Just 1 thing though, you learn integrals in university or college, so you don't need to bother with learning them now. You could if you want, but it would be a lot of extra work.
     
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