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Friction Force and Decelerating Boat

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  1. Jan 22, 2017 #1
    1. The problem statement, all variables and given/known data
    A 1000 kg boat is travelling at 100km/h when its engine is shut off.The magnitude of the frictional force ## \vec f_k## between boat and the water is proportional to the speed v of the boat:##f_k=70v##,where v is in meters per second and ##f_k## is in newtons.Find the time required for the boat to slow to 45 km/h

    2. Relevant equations
    ## \vec F=m \vec a##
    ##v-v_0=at##


    3. The attempt at a solution
    I turned km/h to m/s which its ##100km/h=27.7 m/s## and ##45km/h=12.5m/s##
    then ;
    ##ma=-70v##
    here the connfusing part is ##a## decreases when v decreases.Theres no constant decelaration.I thought integral but without distance I stucked.
    ##∫mdv=∫-70vdt##

    I dont know what to do.

    Thank you
     
  2. jcsd
  3. Jan 22, 2017 #2

    Orodruin

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    Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.
     
  4. Jan 22, 2017 #3
    I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue
     
  5. Jan 22, 2017 #4

    cnh1995

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    That's not the correct equation. You need to separate the variables.
    So you can do integrals and differentials separately, right? I guess your only problem is to set up differential equations using the given data?
    As orodruin pointed out, use a=dv/dt.
    What will be the equation of the force on the boat? Which force is acting on it?
     
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