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Instantaneous Velocity from the graph

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is finding the instantaneous velocity during certain time intervals from the graph.
    p2-03.gif

    Examples of time intervals: 1.1s, 7.4s, 2.7s

    2. Relevant equations

    I know this is the formula for finding the instantaneous velocity

    lim Δv=(Δx/Δt)
    t->0

    3. The attempt at a solution

    I tried locating the points on the curve, by taking two obvious points like 1 on the x and 4 on the y and then making a cross multiplication to find the y in terms of 1.1 and then dividing by the T, since I do not think drawing a tangent to the point is possible here. So, should I use the equation somehow? I made several attempts but they all turned out to be incorrect.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 15, 2012 #2
    According to your graph, there are no "curves", but only straight lines. Recall that on a distance-time graph, the slope is the velocity. The lines' slopes are easy to calculate because they intersect on reasonable numbers.

    So, the slope at 1.1 sec would be equal to the slope at 1 sec or any time within 0-2 seconds.

    Also, at x=1, y does not equal 4, but actually equals 5.
     
  4. Feb 15, 2012 #3
    But isn't the average velocity different than the instantaneous one? Like, I know the slope can represent the average velocity, but is that true on this graph for instantaneous velocity too because it's not a curve?
     
  5. Feb 15, 2012 #4
    Instantaneous velocity is the slope of the line tangent to a point on a curve. Is there really a way to make a line that will be tangent to another line? Not really. Lets say that you can. This 'tangent' line have the same slope as the line it is tangent to, and is actually the same line.

    Lets say that f(x)=4x will be the equation that illustrates the distance of an object. Velocity is the change in distance over the change in time. The change in distance for this function is the slope of the line. Therefore the slope of this line will equal the velocity, both average and instantaneous.
     
  6. Feb 15, 2012 #5
    Yes, that is true. Thank you VERY much for that ^^
     
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