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When will one car overtake the other? (acceleration,veolcity,time)

  1. Apr 17, 2009 #1
    As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0 m/s^2.At the instant the car begins to accelerate, a truck with a constant velcoity of 21 m/s pass in the next lane.

    (a) How far will the car travel before it overtakes the truck?
    (b) How fast will the car be travelling when it overtakes the truck?

    Calculations (a) :

    Car:
    Vi = 0 m/s
    Vf = ?
    Acceleration = 6.0 m/s^2

    Truck:
    Vi = 21 m/s
    Vf = 21 m/s
    Acceleration = 0 m/s^2


    * in order to figure out (a), the deltaD's of both the car and truck must be equal
    - i'm not to sure if the deltaT will be the same but it seems as though the intial time is the same

    This is all I know so far; I've been trying to sub in equations but nothing seems to work. Could someone please guide me in the right direction. Thanks :)
     
  2. jcsd
  3. Apr 17, 2009 #2

    CompuChip

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    Can you write down equations for the distance covered by the car and the truck as a function of time?
     
  4. Apr 17, 2009 #3
    The equations I could use are:
    deltaD = [(vi + vf)/2] x deltaT
    delta D = vi x deltaT + 0.5 x acceleration x deltaT^2
    deltaD = vf x deltaT - 0.5 x acceleration x deltaT^2
    deltaD = (vf^2 - vi^2)/(2 x acceleration)
     
  5. Apr 17, 2009 #4

    CompuChip

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    I suggest first calculating after what time the car overtakes the truck, so find the delta T.

    For the truck, you know the average velocity and there is no acceleration. For the car, you know the acceleration and initial velocity. Which two of the four formulas do you think are useful then?
     
  6. Apr 17, 2009 #5
    For the truck:
    deltaD = [(vi + vf)/2] x deltaT

    For the car:
    delta D = vi x deltaT + 0.5 x acceleration x deltaT^2

    Would I use these two?
     
  7. Apr 17, 2009 #6

    CompuChip

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    What is vi for the car?
    What equation to you get for deltaT?
    What is its solution?
     
  8. Apr 17, 2009 #7
    For the truck:
    deltaD = [(vi + vf)/2] x deltaT
    deltaT = 2deltaD/(vi+vf)

    For the car:
    delta D = vi x deltaT + 0.5 x acceleration x deltaT^2
    how would I rearrange this one?

    *** how would I solve for these without knowing the deltaD value?
     
  9. Apr 17, 2009 #8

    CompuChip

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    You will get a quadratic equation, which should be easy to solve because you already know one solution (the one you don't want).
     
  10. Apr 17, 2009 #9
    You said to first solve for time but in order to do so, the equations ask for a value for deltaD. Are you saying I would get a quadratic equation for time?

    For the car:
    deltaD = 3deltat^2

    For the truck:
    deltaD = 21deltat

    Is this what I was supposed to do?

    Next I changed the equations to deltaT = and then I put one equal to the other.

    deltaD/3 = deltaD^2/21
    = 441/3 = deltaD
    = 147 m

    Is this correct?
     
    Last edited: Apr 17, 2009
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