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Homework Help: Resistance to motion

  1. Mar 23, 2006 #1
    Any got any ideas of how to go around this question? Thanks

    A car of mass m is moving along a horizontal track with speed U>uc when it runs out of fuel. The retarding force due to air resistance is equal to
    (i) [tex] \mu u^2 [/tex] for speed u>uc
    and (ii) [tex] \lambda u [/tex] for speed u<uc

    By writing Newton's second law in the form

    ma = mu du/dx = retarding force
    where x is distance travelled.

    Find the distance travelled without fuel
  2. jcsd
  3. Mar 23, 2006 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Use energy. The car stops when its energy runs out.

    [tex]\int_{u}^{0} Fdx = m\int_{u}^{0} udu = m\int_{u}^{u_c} udu + m\int_{u_c}^{0} udu[/tex]

    By inserting the expressions for u evaluate the two integrals.

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