Question

1. make those assumptions and draw the line of the graph. label the line, “walking dude.”
2. what does the notation δt mean and what is δt between 5 s and 8 s?
3. what does the notation δx mean and what is δx on the graph between 5 s and 8 s?
4. what relation can you use to find the slope of the graph, in terms of rise and run?
5. what quantity represents rise on our graph? what represents run?
6. what equation would you use to determine the slope of a position vs. clock - reading graph? (do not use any numbers yet, simply state the equation.) does this equation look familiar? if not, it is wrong; if so, where have you seen it before?
7. apply the equation and determine the slope of walking dude’s position vs. clock - reading graph.
8. on the axes on the front, plot position vs. clock reading for the two other little dudes shown below. (running dudette starts at 0 m at 0 s; reading dude starts at 8 m at 0 s.) don’t forget to label the plots!
9. what would a line with a shallower slope than that of walking dude mean?
10. what would a line with a negative slope mean?
11. what would a vertical line on the position vs. clock reading graph mean?
12. draw a line parallel to the position vs. clock reading graph of walking dude, but starting at (0 s, 8 m). it’s the graph for walking dude ii. what was different about walking dude ii?

Explanation:

Step1: Define $\Delta t$

$\Delta t$ represents the change in time. For the time - interval between $t_1 = 5s$ and $t_2=8s$, $\Delta t=t_2 - t_1$.

Step2: Calculate $\Delta t$

$\Delta t=8s - 5s=3s$.

Step3: Define $\Delta x$

$\Delta x$ represents the change in position.

Step4: Determine slope formula

The slope $m$ of a graph in terms of rise and run is $m=\frac{\text{rise}}{\text{run}}$. In the context of a position - vs - time graph, the rise is $\Delta x$ and the run is $\Delta t$, so the slope formula for a position - vs - clock reading graph is $m = \frac{\Delta x}{\Delta t}$.

Step5: Analyze meaning of slopes

A shallower slope than that of Walking Dude means a slower speed. A negative slope means the object is moving in the negative direction (backwards). A vertical line on a position - vs - clock reading graph means an infinite speed (instantaneous change in position). A line parallel to the position - vs - clock reading graph of Walking Dude starting at $(0s,8m)$ means Walking Dude II has the same speed as Walking Dude but starts at a different initial position.

Answer:

1. $\Delta t$ means change in time. $\Delta t$ between $5s$ and $8s$ is $3s$.
2. $\Delta x$ means change in position. (No information to calculate $\Delta x$ between $5s$ and $8s$ given in the problem setup).
3. The relation for slope is $m=\frac{\text{rise}}{\text{run}}$.
4. Rise is $\Delta x$, run is $\Delta t$.
5. The equation is $m=\frac{\Delta x}{\Delta t}$, which is similar to the average - velocity formula.
6. (No data to calculate the slope of Walking Dude's graph).
7. (Requires graph - plotting which cannot be done in this text - based format. But the general idea is to plot position on the y - axis and clock reading on the x - axis for Running Dudette starting at $(0m,0s)$ and Reading Dude starting at $(8m,0s)$).
8. A slower speed.
9. Movement in the negative direction.
10. Infinite speed (instantaneous change in position).
11. Walking Dude II has the same speed as Walking Dude but starts at an initial position of $8m$ at $t = 0s$.