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Homework Help: A basic velocity/distance traveled problem (need work checked)

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data
    A car starts from rest and reaches a velocity of 100 km/hr after accelerating uniformly for 10 seconds. how far has the car gone? what is its average velocity?


    2. Relevant equations



    3. The attempt at a solution
    so since this car accelerates uniformly, i assume that it means it has a constant acceleration, meaning the velocity is a linear equation. converting the final velocity to m/sec, i got 250/9 m/sec.

    the slope of this line is then 25/9 (using equation for slope, (y_2-y_1)/(x_2-x_1), plugging in values of 250/9 for final velocity and 0 for initial, 10 for final time and 0 for initial).

    then the equation for velocity is then (25/9)t.
    so,
    distance=integral of (25/9)t from t=0 to t=10, yielding an answer of 1250/9 meters, or about 138.89 meters.

    for the second part, i just divide this integral by the difference of the two endpoints of the interval; namely 10 and 0.

    avg value = integral of (25/9)t from 0 to 10, divided by 10.
    this gives me the average velocity, 13.89 m/sec.

    am I on the right track here?
     
    Last edited: Sep 23, 2010
  2. jcsd
  3. Sep 23, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me.
     
  4. Sep 23, 2010 #3
    EDIT: already checked, never mind. I personally find the equations of motion simpler for a situation such as this, but if that's how feel more comfortable go for it.

    My answers agree with yours and so I'd say it looks good.
     
  5. Sep 23, 2010 #4
    this is true, jarednjames, but i find it a lot simpler to use calculus... just my mindset at least. :P

    thanks for the responses!
     
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