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Simple volocity problem

  1. May 19, 2008 #1

    jk4

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    1. The problem statement, all variables and given/known data
    How long does it take an automobile traveling 60.0 km/h to become even with a car that is traveling in another lane at 40.0 km/h if the cars' front bumpers are initially 125 m apart?

    2. Relevant equations
    [tex]v_{average} = \frac{\Delta x}{\Delta t}[/tex]

    3. The attempt at a solution
    I'll just give an explanation because it seems like a pretty simple problem. I'm just getting a different answer than the book. Here goes:
    I set the distance for the 60km/h car to d+125m since it has to travel the same distance as the 40km/h car plus the extra 125m that it had to catch up. Then I solved them for the variable (d) and set the 2 equations equal to each other, and then finished solving for time.
    I ended up with: 6.25 seconds The book says it takes: 22.5 seconds
    the books answer seems wrong to me... can anyone verify this, or let me know what I did wrong? Thank you.
     
  2. jcsd
  3. May 19, 2008 #2
    22.5 s is correct; i'm not sure what went wrong with your calculations.. they sound about right.
    The easiest way to do this: imagine that the 40 km/h car is stationary (move to its reference frame), initially 125 m from the 60 km/h car.
    What velocity is the 60 km/h car going in this new reference frame (hint: whats the difference in their velocities).
    How long will it take to close the 125m distance at that speed?
     
  4. May 21, 2008 #3

    jk4

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    I was getting the units wrong. Thanks for you help.
     
    Last edited by a moderator: May 21, 2008
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