Figure P2. I shows a motion diagram of a car traveling down...

Figure P2. I shows a motion diagram of a car traveling down a street. The camera took one frame every second. A distance scale is provided. a. Measure the $x$ -value of the car at each dot. Place your data in a table, similar to Table $2.1,$ showing each position and the instant of time at which it occurred. b. Make a graph of $x$ versus $t,$ using the data in your table. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.

Figure P2. I shows a motion diagram of a car traveling down a street. The camera took one frame every second. A distance scale is provided. a. Measure the $x$ -value of the car at each dot. Place your data in a table, similar to Table $2.1,$ showing each position and the instant of time at which it occurred.
b. Make a graph of $x$ versus $t,$ using the data in your table. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.

Key Concepts

Motion Diagram

A motion diagram is a graphical tool that represents an object's positions at successive, equally spaced time intervals. Each dot on the diagram indicates where the object was at a specific moment, providing a visual summary of the object's motion over time.

Data Table Construction

Creating a data table involves systematically recording the measured values, such as the positions of an object and their corresponding times. This organized presentation of data makes it easier to analyze and later graph the relationships between different quantities.

Graphing Position versus Time

Graphing position versus time involves plotting the position on one axis and time on the other to visualize the object's motion. In cases where data points are recorded only at discrete time intervals, the graph is made up of individual dots rather than a continuous line, emphasizing that these points represent specific measurements taken at regular intervals.

Uniform Time Intervals

Uniform time intervals refer to the consistent spacing between observations, which is critical in accurately capturing and representing motion. This regular sampling ensures that the progression of the object’s position over time can be effectively analyzed, facilitating further calculations like average speed or acceleration.

Transcript

00:01 Okay, so for this question, the key concept here is extracting two dimensions of information from a position plane.

00:11 So to start off, we basically have an axis here, and we have position marked zero on one end and 100, 1 ,200 on the other end.

00:28 So these are in meters.

00:30 And we see a bunch of dots and the dots have errors in between them.

00:38 And each dot represents the position of the car after one second.

00:44 So as the car moves from 1 ,200 meters to its next position, one second has passed.

00:53 Okay, and we have a whole bunch of these with different spaces along our position line here.

01:00 And the first aspect of this problem is to extract this information into a usable graph.

01:07 So let's start right off with sketching this out.

01:11 So we know that we're going to have things our first entry time, and that's going to be in terms of seconds.

01:21 And our second side of the column is going to be our position.

01:27 This is an x number line, and it's in terms of meters.

01:33 Okay, so all we have to do is look at our diagram and count and basically record the positions of each of these dots, knowing that one second has elapsed between each of them.

01:47 So first dot here is at the zero mark, so no time has elapted, and so we know that at time zero, we are at position 1 ,200 meters.

02:01 The car after one second has moved to a new position and referencing the diagram in the textbook, we can see that that's probably approximately at 950.

02:14 Moving on to the next dot, another second is elapsed and now we've been traveling for two seconds.

02:22 And seeing where that corresponds on this particular number line, it's around 810.

02:29 And we're just going to carry this on.

02:33 So at three seconds, we see the car is at maybe 750.

02:40 Four seconds.

02:42 We're at about 700.

02:45 Five seconds.

02:47 That's about 650.

02:50 Six seconds.

02:53 We're at 600...