Very simple calculus problem graphs and velocity/time graphs to acceleration.

  1. 1. The problem statement, all variables and given/known data
    I'm studying for a Calculus test and I am having trouble on a problem. And who better to ask than the members of physicsforums!?

    Basically, we are studying average acceleration, velocity, secant and tangent lines. We are given the graph of a function, and its corresponding data points.

    The question asks:
    "Find the average acceleration of the car, in f/s, over the interval 0<t<50.(The inequality signs are acutally "less than or equal to", but I don't know how to input such characters.)

    I'm aware that the derivative of a velocity time graph is its acceleration/time graph. So I assume that the slope of the line is the acceleration. Unfortunately, we are not permitted to fit a best line, or derive an equation. Is there another way of doing this? Thanks for any help.
     
  2. jcsd
  3. EnumaElish

    EnumaElish 2,483
    Science Advisor
    Homework Helper

    Think about it this way: derivative is essentially the limit of dy/dx where "dy" stands for the change in y (e.g., from one data point to the next). Similarly for x. How would you apply dy/dx when the change isn't "infinitesimal" (i.e. limit)?

    To recap:
    Instantaneous change = derivative = we take the limit
    Average change = ratio = we do not take the limit
     
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