Vectors around a circular track

[seanlindo06]

A jogger runs around a 2 km circular track as shown below. Using graph paper, draw a displacement - time graph of the continuous North vector which runs from the start axis to the jogger's current position. Identify the shape of your graph. Draw a corresponding distance - time graph for the jogger's, overall distance covered. Label important points between the 2 graphs.


circular distance time
(m) (s)
0 0
250 60
500 130
750 185
1000 245
1250 303
1500 366
1750 437
2000 501

also included is a circle with a perp. line inside of it
. The point on the right side of the circle is labeled start/finish. Any clue on how to do this?

 

[HallsofIvy]

You are told that the track is a "2 km circular track" so I assume that "2 km" is the length. I suspect that this problem is preparation for "harmonic motion" and that you are not expected to do detailed calculations with trig functions.

Here's what I would do. Since the circle given is not actually 2 km long (!) figure out how long it really is (measure its diameter and multiply by pi) 2km/actual length is the factor you will need. I might actually take a strip of paper as long as the circle you are given and mark off, say, 1/4, 1/2, 3/4, 1, 1 1/4, etc. km on it. (since the track is actually 2 km long, 1/4 km will be 1/8th of your strip of paper, etc.)

Now use your strip of paper to actually mark the postions given on the circle. 0 m will, of course, be whatever starting point you want (perhaps on the right would be best), 250 m= 1/4 km will be 1/8 of the way around the circle, 500 m= 1/2 km will be 1/4 of the circle, etc.

NOW measure just the "height" of each of those marks from you starting point (if you made you starting "on the right", that is horizontally with the center of the circle, you will be measuring only the vertical distance. That's "north". Now make a graph using the time values you are given as the x-axis and the corresponding vertical distances you have measured as the y-axis. That will be a very rough graph of course, but you should be able to recognize what type of function it corresponds to (I gave you a hint above).

 

[wais]

The displacement-time graph for the continuous North vector would be a straight line with a positive slope, starting at the origin and ending at the point (2000, 501). This is because the jogger is continuously moving in a northward direction and the displacement is increasing with time.

The shape of the graph would be a diagonal line, indicating a constant velocity of the jogger. This is because the jogger is running at a constant speed around the circular track, which results in a constant displacement over time.

The corresponding distance-time graph for the jogger's overall distance covered would be a curved line, starting at the origin and ending at the point (2000, 2000). This is because the jogger is covering a longer distance with each lap around the track, resulting in a curved graph.

Important points on the graphs would include the start/finish point at (0,0), the point where the jogger completes one lap at (2000, 2000), and the points where the jogger reaches the 250m, 500m, 750m, 1000m, 1250m, 1500m, 1750m, and 2000m marks.

To draw the graphs on graph paper, you can use the horizontal axis to represent time and the vertical axis to represent displacement or distance. Each unit on the axis can represent a certain amount of time or distance, depending on the scale you choose. Then, plot the points given in the table and connect them with a line to create the graph.