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Could someone give me two questions relating to that? I have to do it for a project and I don't get it AT ALL.

Thanks!

2007-01-07 04:24:42 · 3 answers · asked by halloweenfallchild 2 in Science & Mathematics Physics

3 answers

what is the area under a graph of distance vs time called?
what is the area under a graph of velocity vs time called?

2007-01-07 04:38:41 · answer #1 · answered by Dr W 7 · 1 0

OK.

Area under a right triangle (RT) = A = 1/2 bh; where h = the height of the RT and b = the base of the RT; so that the slope of the hypoteneuse = m = h/b.

Now, v = y/t; where v = velocity, y = a distance traveled in time t. v = y/t looks similar in form to m = h/b, which is the slope of a RT. In fact, on an x-y (Cartesian) graph, if you set h = y and b = t, you could find the slope for any given distance traveled (y) in a time (t). That is, the slope of that RT is the velocity.

Now, back to the area inside that right triangle = 1/2 bh. If we assign h = v and b = t; where v = velocity and t is the time expired at v, then A = 1/2 bh = 1/2 tv; so that 2A = vt = S, which is the distance S traveled in time t at a velocity v. Thus, two times the area of the right triangle equals the distance something would travel at velocity v over time t.

In general, the area of an x-y graph (e.g., A = xy) represents a product of the xy coordinate values.

Here are a couple of questions:

1. If your x-y coordinates (measured from 0,0) are x = 10 seconds and y = 20 meters, find the slope of the right triangle formed by these coordinates. What does this slope represent in the real world?

2. Using the results of question 1, how would be the distance (S) covered in 20 seconds be represented on an x-y graph? Give the x-y coordinates measured from (0,0) and show how this representation is equivalent to distance covered.

2007-01-07 13:01:03 · answer #2 · answered by oldprof 7 · 0 0

use the antiderivative if ur given a velocity graph. use the antiderivative twice if ur given acceleration. if you have a ti 83 or 84 graph the original equation and go to 2nd+calc, click option 7, and enter your limits. email me if u need more help.

2007-01-07 12:42:43 · answer #3 · answered by venusvakhshori 2 · 0 0

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