FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at (c) t = 30s

Video transcript

Hello everyone. Let's go through this practice problem below is a position time graph of a subway train traveling from London to Edinburg. Find the train's velocity at T equals 20 seconds. Option A 9.21 m per second. B 4.45 m per second. C 6.67 m per second and D 3.21 m per second. This is a pretty simple speed problem with a little bit of graph analysis in there. The important thing to recall here is that velocity is the rate of change of position in terms of graph analysis. That means that if we have a graph of position with respect to time, then the velocity is the slope of that graph. This problem specifically is asking us to evaluate the velocity at the time 20 seconds which hits this point right here that I'm highlighting in red on the graph. And if we look at the graph, we can see that this point is part of a longer segment that appears to be linear, a straight line. So if we want to find the slope or the rate of change of the train's motion at this point, we can use the information given by the graph to find the rate of change of position over this interval. So recall that velocity can be numerically calculated as a change in position such as the final position minus initial position divided by a change of time, such as a final time divided by an initial time for the interval. And the graph that I've highlighted in red, these values can be read pretty easily. The final position is 350 m. So 350 m for X sub two minus an initial position of 100 and 50 m divided by the final time, 40 seconds for that interval, see minus the initial time of 10 seconds for that interval. If we put this into a calculator, then we find a velocity of about 6. m per second. So this is our answer. If we look at our multiple choice options, we can see that this agrees with option C so option C is the correct answer to this problem. And that is all for this problem. I hope this video helped you out and please consider checking out some of our other videos which will give you more experience with these types of problems. That's all for now. And I hope you all have a lovely day. Bye bye.