Position/Displacement/Distance (2/3)
On the right side of this photo, I use our equation Δx = x-x˳ to find the displacement of a trip from Norman, Okla to Davis, Okla using their mileposts on I-35 as guides. This is a displacement of -53 miles.
Our return trip is in the other direction, so it is +53 miles.
An important point of this map is that 108 and 55 (the positions of Norman and Davis) only have meaning with respect to a reference point. That reference point is ARBITRARY.
Oklahoma calls mile zero its boarder with Texas along the Red River. So Davis is 55 miles north of that and Norman is 108 miles north of that.
Texas would not like this reference frame, because it would make all Texas mile markers negative. So they pick a different reference frame- they call the boarder with Mexico mile zero. We could renumber all the Oklahoma miles by simply adding the total Texas miles to the Oklahoma numbers.
If we do this, as I did on the left, and then travel from Norman to Davis, I still displace -53 miles. Going back north I still displace 53 miles.
Of course I do! Towns don't get up and move because I chose to measure them differently. Once again, the laws of physics and measuring motion get us displacement. To decide on position, we need a reference point that we measure from. Apparently, this reference point is arbitrary. You pick a convenient one for you. We did this in our first lab by calling the starting line zero meters. The only rule is that once you pick a reference point, you need to stick with it throughout the problem.
Another thing worth noting is at the far right. My displacement for a round trip between the two cities (regardless of reference frame is -53 mi + 53 mi = 0.
Since direction matters for displacement, and in a round trip you finish where you started, displacement for such a trip always adds to zero.
Clearly, another number is important, though. After driving this trip, you are tired. You spent gas and there's wear and tear on your car. So if you add up the absolute value of displacement, you get what's called distance. For this round trip, the distance is |Δx| = |-53| + |53| = 106mi
Position/Displacement/Distance (2/3)
On the right side of this photo, I use our equation Δx = x-x˳ to find the displacement of a trip from Norman, Okla to Davis, Okla using their mileposts on I-35 as guides. This is a displacement of -53 miles.
Our return trip is in the other direction, so it is +53 miles.
An important point of this map is that 108 and 55 (the positions of Norman and Davis) only have meaning with respect to a reference point. That reference point is ARBITRARY.
Oklahoma calls mile zero its boarder with Texas along the Red River. So Davis is 55 miles north of that and Norman is 108 miles north of that.
Texas would not like this reference frame, because it would make all Texas mile markers negative. So they pick a different reference frame- they call the boarder with Mexico mile zero. We could renumber all the Oklahoma miles by simply adding the total Texas miles to the Oklahoma numbers.
If we do this, as I did on the left, and then travel from Norman to Davis, I still displace -53 miles. Going back north I still displace 53 miles.
Of course I do! Towns don't get up and move because I chose to measure them differently. Once again, the laws of physics and measuring motion get us displacement. To decide on position, we need a reference point that we measure from. Apparently, this reference point is arbitrary. You pick a convenient one for you. We did this in our first lab by calling the starting line zero meters. The only rule is that once you pick a reference point, you need to stick with it throughout the problem.
Another thing worth noting is at the far right. My displacement for a round trip between the two cities (regardless of reference frame is -53 mi + 53 mi = 0.
Since direction matters for displacement, and in a round trip you finish where you started, displacement for such a trip always adds to zero.
Clearly, another number is important, though. After driving this trip, you are tired. You spent gas and there's wear and tear on your car. So if you add up the absolute value of displacement, you get what's called distance. For this round trip, the distance is |Δx| = |-53| + |53| = 106mi