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 (b) constant and positive?

Question

Position-time graph showing a professor's movement with labeled points a to f.

Accepted Answer

Hey everybody. So today we're dealing with the problem regarding a position versus time graph. Now we're being told that an office messenger leaves a waiting area to deliver a parcel to his client. Now the office Messenger reaches the client's place after 12 minutes and returns back to the waiting area. The messengers distances plotted in the graph below. As we see it is a position versus time graph. And we're being asked to determine which points represent both constant and positive velocity. So let's dive into this a little deeper. Right. So very important to note is that on a position versus time graph on a position versus time graph the slope, right? If we want to find the slope, we would take the change in the y direction of the graph divided by the change in the X direction of the graph. So in that case it would be the change in the uh position over the change in time. And what does this mean? Well, change in position over change in time is the definition of velocity velocity, which means the slope at any given point on a position versus time graph is equal to the velocity at that specific point. With that in mind. Let's go ahead and delve a little further. So what we need to note is that constant velocity, constant velocity means that we have a straight line constant. Let's try this in blue. Let's write this in blue constant velocity means we have a street line. Because when the slope of a line is straight, that means it is the same at each point going up, which means the velocity in this case would be constant. If we're looking for a positive velocity, positive velocity, positive positive velocity, then the sign must be positive, right? It needs to be an upper trend. The velocity needs to be a positive value, not just in magnitude, but in actuality of its value itself. And that means that the slope must also be a positive slope. It must be going in the upwards direction, it must be going upwards. So with that knowledge, we can actually rule out three of the points on the graph. Right away, points D. E and F can all be ruled out because D has a velocity of zero because the slope is zero, which means it's neither positive nor negative. And points E N F r downwards, they have a negative slope, which means they cannot fit our criteria. Now looking further, if we want constant velocity between choices A B and C, we can actually rule out and to choice A why? Because it is a curve. It's parabolic in nature, which means it cannot be constant. It is changing at each point along the curve. However, on points B and C. B is a straight line and see as a straight line and both B and C are positive in direction. Therefore the points that represent constant and positive velocity on this graph on this position versus time graph, I should say our points B and C or answer choice D Oops answer choice D. I hope this helps, and I look forward to seeing you all in the next one.

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 (b) constant and positive?

Verified Solution

Key Concepts

Velocity

Position-Time Graph

Intervals of Motion