Distance-function and velocity-function problem

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In summary, the problem involves a distance function with a constant velocity and starting position, and the velocity is represented by [B] and [C] in different cases. The slope of the graph is represented by [E], and when [F] (the velocity) is negative, the graph of [G] (the distance function) goes downward and the area in the v-graph counts as [H]. The forward and backward motion can be determined using [I] and [J], respectively, and the distance function for a specific time interval is represented by [K].
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Matthewkind
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The problem is three paragraphs with a bunch of blank spots.

Starting from f(0) = 0 at constant velocity v, the distance function is f(t) = __[A]__. When f(t) = 55t the velocity is v = ____. When f(t) = 55t + 1000 the velocity is still __[C]__ and the starting value is f(0) = __[D]__. In each case v is the __[E]__ of the graph of f. When __[F]__ is negative, the graph of __[G]__ goes downward. In that case area in the v-graph counts as __[H]__.

Forward motion from f(0) = 0 to f(2) = 10 has v = ____. Then backward motion to f(4) = 0 has v = __[J]__. The distance function is f(t) = 5t for 0 <= t <= 2 and then f(t) - __[K]__.

_____________________________________________

There's more to the problem than this, but [K] is where I get stuck, not understand the problem. My answers thus far are:
[A] = vt, = 55, [C] = 55, [D] = 1000, [E] = slope, [F] = v, [G] = f, [H] = f, = 5, [J] = 0.

First, am I doing this correctly? And second, what precisely is K asking me for?
 
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  • #2
Matthewkind said:
The problem is three paragraphs with a bunch of blank spots.

Starting from f(0) = 0 at constant velocity v, the distance function is f(t) = __[A]__. When f(t) = 55t the velocity is v = ____. When f(t) = 55t + 1000 the velocity is still __[C]__ and the starting value is f(0) = __[D]__. In each case v is the __[E]__ of the graph of f. When __[F]__ is negative, the graph of __[G]__ goes downward. In that case area in the v-graph counts as __[H]__.

Forward motion from f(0) = 0 to f(2) = 10 has v = ____. Then backward motion to f(4) = 0 has v = __[J]__. The distance function is f(t) = 5t for 0 <= t <= 2 and then f(t) - __[K]__.

_____________________________________________

There's more to the problem than this, but [K] is where I get stuck, not understand the problem. My answers thus far are:
[A] = vt, = 55, [C] = 55, [D] = 1000, [E] = slope, [F] = v, [G] = f, [H] = f, = 5, [J] = 0.

First, am I doing this correctly? And second, what precisely is K asking me for?

[J] is incorrect. The others are correct.
 

FAQ: Distance-function and velocity-function problem

1. What is a distance-function problem?

A distance-function problem is a mathematical concept that involves finding the distance between two points on a coordinate plane. This can be solved using the distance formula, which takes into account the coordinates of the two points and calculates the distance between them.

2. How is a velocity-function problem different from a distance-function problem?

A velocity-function problem involves finding the velocity, or rate of change of distance, between two points on a coordinate plane. This can be solved using the velocity formula, which takes into account the change in distance and the change in time between the two points.

3. Can a distance-function problem be solved without using the distance formula?

Yes, there are other methods for solving distance-function problems, such as using the Pythagorean theorem. However, the distance formula is the most commonly used method as it is a straightforward and efficient way to calculate the distance between two points.

4. What are some real-life applications of distance-function and velocity-function problems?

Distance-function and velocity-function problems are commonly used in physics and engineering to calculate the distance and velocity of moving objects. They are also used in navigation systems, such as GPS, to determine the distance and velocity of a moving vehicle.

5. How can distance-function and velocity-function problems be visualized?

Distance-function and velocity-function problems can be visualized using a coordinate plane or graph. The two points can be plotted and the distance or velocity can be represented as the slope of a line connecting the two points. Alternatively, they can also be visualized using motion diagrams or animations.

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