FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at (a) t = 5s

Video transcript

Hey, everyone. Let's go through this practice problem. Chloe walks to her school daily which is 300 m from her home using her position time graph. Find the velocity at T equals 500 seconds. Option A 15 m per second, option B 5 m per second, option C 10 m per second and option D m per second. So this problem has us looking for the velocity of her motion at the 502nd mark on the graph which corresponds to right about here on the curve. And keep in mind recall that when we have a graph of position with respect to time velocity is defined as the slope of that graph. But what you might notice just from kind of eyeballing this graph is that at that point on the graph, the line looks flat, it looks like there's no slope at all. So right off the bat, it kind of looks like the answer to this problem is going to be 0 m per second because it doesn't look like the position is changing. It doesn't look like there's any rate of change at that point on the graph. But to confirm this we can do this more rigorously more mathematically by using the slope equation. So V can be written more mathematically as if we choose two different points, two different positions for two different points in time. Then the slope and in our case, the velocity is equal to the final position. So X sub two minus the initial position X sub one divided by the final time T sub two minus the initial time T sub one. So since we're looking for the rate of change at this point in the graph, let's choose two different points kind of around the point we're looking at and see what slope we find for that. So I'll choose the points where time is equal to 400 seconds and 600 seconds and analyze those points for all three points. The position seems to be 200 m. So X sub two is 200 m an X of one is also 200 m, nothing has changed there T sub two is 600 seconds minus T sub one, which is 400 seconds since minus 200 is obviously zero. This whole answer goes to zero. So that's 0 m divided by the 600 minus 400 is 200 seconds. Zero, divided by 200 is just zero. And we're left with a speed, a velocity of 0 m per second. So that is our answer after all. And this matches up with option D which states 0 m per second. So option D is our answer to the problem and that is it for this video. I hope this video helps you out. Please consider checking out some of our other videos which will give you more experience with these types of problems, but that's all for now and I hope you all have a lovely day. Bye bye.