# Straight-Line Graph: x/t2 and t or x/t Pairs for Plotting

• recon
In summary, when a stone slides across an icy surface with uniform retardation, the distance traveled can be represented by the equation x = v_0t + 0.5at^2. This means that the plotted graph of axes x and t2 would result in a straight line. The same is true for x/t and t, as well as x/t2 and t. However, the graph of axes x/t2 and t would result in a flat line, as the constant acceleration would cause a constant decrease in velocity. Ultimately, this means that options B, C, and E would all result in a straight-line graph.
recon
A stone slides across an icy surface and travels a distance of x in time t while suffering uniform retardation. Which of the following pairs of quantities, plotted to represent the motion of the stone, would give a straight-line graph?

A. x and t
B. x and t2
C. x/t and t2
D. x/t and t
E. x/t2 and t

This is my approach to the problem:

The initial velocity, u = at.

Hence, the distance traveled by the stone, x = 0.5at2

x/t2 = (0.5at2)/t2

= 0.5a

Since a is a constant, then a flat line would be represented in a graph of axes x/t2 and t.

Also, in D., x/t = v, which decreases at a constant rate because of the constant deceleration, so this is another straight-line graph.

Obviously, there must be something wrong with my reasoning because there can only be one, and not two answers for each multiple choice question.

recon said:
The initial velocity, u = at.

Hence, the distance traveled by the stone, x = 0.5at2

Are you sure that's the full equation for position as a function of time? What about the initial velocity?

x = at(t) + 0.5 at2
= 1.5 at2 ?

This does not seem right.

Have you ever seen the formula:

$$x=v_0t+\frac{1}{2}at^2$$

## 1. What is a straight-line graph?

A straight-line graph is a graphical representation of a linear relationship between two variables. It is a visual representation of how one variable changes in relation to the other, with a constant rate of change.

## 2. What is the significance of x/t2 and t or x/t pairs in plotting a straight-line graph?

The pairs x/t2 and t or x/t are used to plot a straight-line graph because they represent a linear relationship between two variables. The x/t2 pair represents the variable x divided by the square of the variable t, which is equivalent to the inverse of the variable t. The t or x/t pair represents the variable t or the variable x divided by the variable t. These pairs help to create a linear relationship between the two variables, making it easier to plot a straight-line graph.

## 3. How do you plot a straight-line graph using x/t2 and t or x/t pairs?

To plot a straight-line graph using x/t2 and t or x/t pairs, you will need to have a set of data points for each pair. Then, plot the points on a graph with the x-axis representing the x/t2 pair and the y-axis representing the t or x/t pair. Once all the points are plotted, connect them with a straight line. The resulting graph should be a straight line, indicating a linear relationship between the two variables.

## 4. What does the slope of a straight-line graph represent?

The slope of a straight-line graph represents the rate of change between the two variables. It is calculated by dividing the change in the y-axis (t or x/t) by the change in the x-axis (x/t2). The slope is a measure of how much the dependent variable (t or x/t) changes for every unit change in the independent variable (x/t2).

## 5. How can you use a straight-line graph to make predictions?

A straight-line graph can be used to make predictions by extrapolating the line beyond the plotted data points. This can give an estimate of how the dependent variable (t or x/t) will change if the independent variable (x/t2) continues to increase or decrease. However, it is important to note that these predictions are only accurate if the relationship between the two variables remains linear.

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