Ii figure 2 36 is a position versus time graph for the...

(II) Figure $2-36$ is a position versus time graph for the motion of an object along the $x$ axis. Consider the time interval from $A$ to $B .(a)$ Is the object moving in the positive or negative direction? $(b)$ Is the object speeding up or slowing down? $(c)$ Is the acceleration of the object positive or negative? Now consider the time interval from D to E. $(d)$ Is the object moving in the positive or negative direction? $(e)$ Is the object speeding up or slowing down? $(f)$ Is the acceleration of the object positive or negative? $(g)$ Finally, answer these same three questions for the time interval from $\mathrm{C}$ to $\mathrm{D}$.

Transcript

00:03 In this question, we are analyzing the position time graph that is given to you in your textbook.

00:10 So please make sure you have that handy.

00:12 Now, for the first question, it wants us to analyze the graph in between these portions that i've highlighted here in blue.

00:23 Okay.

00:25 Now, to answer these questions, i kind of find it easiest to draw a velocity time graph first.

00:31 And i'll show you why.

00:34 So first let's draw our velocity time graph.

00:37 So if you notice in between these first two blue lines here on the graph, the graph does this, okay? that's the shape of it, which indicates that the slope starts off with like practically no slope, so no velocity, and then it gets steeper and steeper and steeper, and it's also sloping down.

01:01 So that tells me that this object is speeding up in the negative direction for the first part.

01:07 Then if you look at it in this portion here, that is a constant velocity, a constant negative velocity.

01:16 Okay.

01:17 Then in this portion right here, we have a flat horizontal line, which means that our graph, the object stands still for a time.

01:29 Okay, so it has zero velocity.

01:31 And then in the last portion, so this section here, where the graph kind of curves up like this, that indicates that it is speeding up because if you were to analyze the slope along the graph, it gets steeper and steeper and steeper and steeper over time and it is sloping up.

01:51 Okay, so on the velocity graph, it would be sloping up like that because it's speeding up in the positive direction.

02:00 Okay so now let's go back to looking at just this first section here that i'm circling and it wants to know first if is the object moving in the positive or the negative direction well because this line is sloping down when we were analyzing the slope we know that that is going in the negative direction which is why we drew our velocity graph under the time axis which puts it in the negative quadrant anything above the time axis is the positive quadrant okay so we know that it is going in the negative direction and then to answer the question if it is speeding up or slowing down it is speeding up because the slope gets steeper okay so started with practically a flat slope and then we got a very very steep slope so that indicates that it is speeding up and then it wants to know if the acceleration is positive or negative to figure out the acceleration we need to look at the slope of the line that we drew on our velocity graph and as you can see this line segment here slopes down it has a negative slope so that tells us that our acceleration is negative okay next we want to answer the same questions, but now we are looking at this portion of the graph...

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