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A good problem based on motion

  1. Sep 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Places A and B are 100 km apart on a highway. One car starts from A and the other from B, at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in hour. What are the speeds of two cars?

    2. Relevant equations

    3. The attempt at a solution
    In the first case,
    I assumed that both are travelling toward a point C, and the speeds are x,y respectively(x>y).
    Therefore, If car 2 were made to be still, then car 1 will travel with a speed of x-y
    So, x-y=20 (Speed = Distance/time)

    How can I continue with Case 2?
    Help me out:)
    Last edited: Sep 16, 2014
  2. jcsd
  3. Sep 16, 2014 #2


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    Hello Ajay, and welcome to PF.

    :smile: I liked the sketchtoy. But what you really need are some relevant equations.

    For the first case:
    One for the position of car A as a function of time, and one for the position of car B. Position of point C is where the cars are at the same place. Where that is is not relevant. But you know that at time t=5 hours the equality holds.

    Second case same story, different expression for one of the two positions, different C (again, irrelevant). But at time t = 1 hour the equality holds.

    And now you have two equations with two unknowns, the speeds of the cars. Presto, physics = math !
  4. Sep 16, 2014 #3


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    I would keep to the standard approach.

    When travelling in the same direction, the distance each covers is its speed x duration. That gives you one equation.

    What travelling in opposite directions, the distance each covers is its speed x duration. The other equation.

    Two equations, two unknowns.
  5. Sep 16, 2014 #4


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    is a good start. You don't know the speeds, so you name them va and vb. Position in one dimension can be given as x. And a reference point can be xA=0, so that xB=100 km.

    So, starting from your relevant equation x(t) = x(0) + v * t
    -- this is how you can write your Speed = Distance/time in a convenient way for later use ! --
    (this way it has the look of an equation, as opposed to "conversation" :smile:)​
    you write down the position of car a as a function of time:
    xa(t) = ...​
  6. Sep 16, 2014 #5


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    Gold Member

    Hi Ajay,

    I would start by adding some additional detail to your sketch. Draw out each situation on an X-axis with some labels for your distance, and vector arrows labeled with the velocities va and vb.

    Then work on creating the position equations for each car in each situation, as BvU suggested.
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