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

by TexasCow
Tags: acceleration, calculus, graphs, problemgraphs, simple, velocity or time
TexasCow is offline
Nov1-07, 08:40 PM
P: 40
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.
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EnumaElish is offline
Nov1-07, 09:04 PM
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P: 2,483
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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