A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.10. At which of the labeled points is her velocity (c) constant and negative?

Video transcript

Hey everybody. So today we're given a graph of a man who leaves his house, goes to a local market and comes back. Now he meets an old friend after seven minutes after seven minutes and absconds his journey to the market and they both go back to his house instead. So the man's distance from his house is a function of time as shown below. And we're being asked to determine which points represent constant and negative velocity. So what we need to look for, what we need to look for here is that we're dealing with a position versus time graph. Its position versus time. Now, what does this mean? Well, on a position versus time graph, the slope slope is equal to velocity, right? And we can determine this just by doing simple rise over run. If we do, if we want to find the slope at any point here, we would take the change in the y direction versus the change in the X direction of the graph, which in this case would be the change in position over change in time, which is simply the definition for velocity. So with that in mind, Right. Or rather, yes, exactly. So with that in mind, if we want to separate things, we want constant velocity and we want negative velocity. So a constant velocity means that the curve would be a straight line. Right? So the other thing we're looking for is that if we want a positive slope, if we want or rather if we want a negative velocity, then we have to look at the direction of the slope itself, right? So if the slope is negative, then we will have a negative velocity. So in that regard we can actually rule out anything on the left side before time is equal to seven seconds. And why is that? Well, that's because the instantaneous slope at any one of these points will be positive, which means we'll have a positive velocity, which is not what we're looking for. Now looking at points A, B and C, only two of them are actually straight lines, answer choice B and answer choice A where A is a much steeper slope. However, both A and B are negative slopes right there pointing downwards. So in this regard we can determine that both A and B represent constant and negative velocity or answer choice B. I hope this helps. And I look forward to seeing you all in the next one.