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Nick starts jogging and runs faster and faster for 3 minutes, then he walks for 5 minutes. He stops at an intersection for 2 minutes, runs fairly quickly for 5 minutes, then walks for 4 minutes.
$$\begin{array}{l}{\text { (a) Sketch a possible graph of the distance } s \text { Nick has covered }} \\ {\text t \text { minutes. }} \\ {\text { (b) Sketch a graph of } d s / d t}\end{array}$$

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Okay. So question is giving his next start jogging and run faster for three minutes. Okay, so you run faster for three minutes and he walks for five minutes. Another point is he walks for five minutes. He stops at an intersection for two minutes. Run fair quickly for five minutes again. He ren faire quickly for five minutes and then walks for four minutes. Okay, so this is the data given and we're told toe plot or graph. Distance s verses. Time T. Okay, So let's have our access first. De excess and distance success as so For three minutes, he walks faster and faster, so for three minutes, you'll accelerate after three minutes. So this is time. Three. After three minutes, he walks for five minutes, so it will be a constant speed so we can ever straight lines in spirits constant. Then it stops at an intersection for two minutes. So this is three plus five. That is eight. Andi stops for two minutes, so that will be original alliances. There is no incriminating distance, so it stops for two minutes. So eight plus two will give us then and then he start walking fairly quick. Okay, so again, it's all weekend. It's given running fairly quickly. Okay, so that can be the president came by off a poor train line. Okay, A slope with laden high. And it is done for four minutes, so we can add four minutes. So 10 plus four is 14. So this is the graph or s word says T Okay. And your point we have to remember is since in real life we don't just directly switch from a particular speed toe Another we haven't inertia. So there will be a curvy er. It will be a small transition, and similarly here we'll have a smooth transition. Now we have to plot the diagram or graph for D s by D t. Okay, so we'll have your same time. TXs What says the s pay DT. Okay, so since at time three still time. Three minutes is for increasing his speed on that, assuming it's a constant speed increments. So we will have ah, straight line till time three again after time. Three minutes. He started walking, but this initiation off walking will not start suddenly. Okay, so he starts walking at constant rates, so we'll take it as a horizontal line. And after five minutes, that is it around eight minutes, that is three plus 58 minutes. He stops running or walking. So at that time velocity, This D s by D. T is nothing but velocity is zero. And this change in its velocity from constant walking to zero is not an instant but a gradual process. So we'll have ah, slope like this and the velocity will come to zero and it will remain zero for next two minutes. So that is that time, then. Okay, Now, after 10 minutes again, he starts walking fairly quickly so that walking is four four minutes. So we can again have in cream mint in its velocity. And it's a quick walking so well are a velocity to it. And this working is again not instantaneous. Well, gradually to increase to quick walking. This will go till 14 minutes. Now, the important fact here we have to understand is there is no discontinuity due to sudden stopping or walking. Since in real life we cannot stop instantaneously or start walking incent. Initially, we need we have an inertia. And that is what is represented by this girl. Thank you

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Heather Zimmers

Kayleah Tsai

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Heather Zimmers

Kayleah Tsai

Kristen Karbon

James StewartCalculus: Early Transcendentals

Grace He

Heather Zimmers

Kayleah Tsai

Kristen Karbon

James Stewart

Calculus: Early Transcendentals