Instantaneous Velocity graph problem

  1. Find the instantaneous velocity at 1 s.
    Answer in units of m/s.

    the coordinate for 1s is (1,4)

    How do i find the instantaneous velocity?
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    welcome to pf!

    hi iiskenny! welcome to pf! :smile:
    by differentiating, or by drawing a tangent to the graph …

    but what's the rest of this function? :confused:
     
  4. Velocity is defined as the rate of change of position divided by the rate of change of time.

    This is the same as saying that velocity is the slope of the position vs. time graph.

    Therefore, instantaneous velocity at 1s is the slope of the position vs. time graph at t=1s.
     
  5. HallsofIvy

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    But, as both tiny-tim and Beaker87 have said, just knowing the position is not enough! That's like saying "at 2:00, a car was at 4th st and Central ave. How fast was it going?"!

    You need to know something about it motion through that point. An actual "position function", telling where it was at different times, would be excellent- take the derivative of the function. If you are given a "x versus t" graph, you can estimate the slope of the tangent line at the given point. If you are given a position at another time, before or after this t= 1 you can estimate the speed at t= 1. If you are given the position at times before and after as well as at t= 1, you can get a better estimate.

    Now, what information are you really given? What is the full statement of the question?
     
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