Calculus :

Hello. Please help me answer the rest of question 5 and 6-9 as it is all based on the same question. I have already worked out 5a-f. I know this is a lot but it would be more confusing for other tutors if I uploaded it separately. Please edit the image if you can so it is easier to follow. Thank you so much!

Directions [Continued]: Use the formula D=rt formula to answer the following questions: Distance = Rate * Time 5. (Continued) g] The process of taking better and better approximations of this constant rate of increase in speed is a limiting process. By breaking the interval up into smaller subintervals with a constant speed on each sub-interval, we were able to nd the distance Havelled on each of the sub-intervals and then up the distances to get the total distance travelled. Note that on each sub-interval, to get the total distance travelled on that sub-interval, we computed the under the straight line. Finally, we'll do the same thing on this line. To get the total distance travelled for the driver that increases their speed at a constant rate, compute the under the slanted 90T 80 line. Total distance travelled: Directions (Continued): Use the formula D=rt formula to answer the following questions: Distance = Rate * Time 7. Apply the concept you just learned in #5 to compute the total distance travelled for the driver 0 0 0 0 whose speed is given in die graph below: 0T l l l l l l /,, 10 V ) Total distance travelled: 2 hr 4 hrs 6 hrs 6. Apply the concept you just learned in #5 to compute the total distance travelled for the driver whose speed is given in the graph below: Speed (in km/h) Total distance travelled: 8. Use the speed vs. time graph shown to ll in the table of values for the total distance travelled at each point in time. . Distance Travelled _) 2 hr 4 hrs 9. Use the table you made above to ll in the distance vs. time giaph shown at the right a) In general, how is distance traveled related to velocity? b] If you graphed the derivative function for the graph you just made, what would it look like? Directions (Continued): Use the formula Dart formula to answer the following questions: Distance = Rate * Time 5. (Continued) d) Suppose the driver performed even more (unrealistic) jumps in speed as shown in the graph below. How far would the driver have travelled altogether? 90 90 km 80 70 75 km Speed 60 (in km/h) Lookm 50 40 45 km 30 30 km 20 15 + 30 + 45 + 6 0 + 75 + 90 10 15 km = 315 kml 2 hrs 4 hrs 6 hrs Total distance travelled with these 6 jumps: 315 km e) How does this driver's (with 6 jumps) total distance compare to the driver with only three jumps and the original driver (the one that increased their speed gradually rather than suddenly jumping speeds)? this driver has an even closer approximation to the total distance traveled by the original driver . f) On the axes below, make a sketch of what it would look As the number of like if the driver had made 12 jumps, and 24 jumps in speed. intervals increases, 12 jumps 24 jumps the graph begins to more and more Speed Speed closely resemble (in km/h) (in km/h) the graph of the original straight line. This is a process. Time TimeDirections (Continued): Use the formula Dart formula to answer the following questions: Distance = Rate * Time 5. In the graph shown below, a driver starts at 0 km/h and then over half an hour, they gradually increase their speed (at a constant rate) until they reach 90 km/h. How far did the driver travel in that 6 hours? Work through the steps below to build your intuition. 90 80 6hr . 90 km / hr 70 540 kmi Speed 60 (in km/h) 50 40 30 20 10 2 hrs 4 hrs 6 hrs a) Did the driver go more than, less than, or equal to 540 kilometers? Explain your reasoning. The driver went less than 540km because the driver must drive at 90 km / hr for le hours straight to Travel 540 km b) Suppose instead of 90 gradually increasing 80 the . 90 km speed, the driver 70 - 180 km performed (unrealistic) 60 jumps in speed as shown in the graph at the right. 50 the . lookm How far would the 40 - 170km driver have travelled 30 altogether? 20 2 hr . 30km 3120 kim 10 = W0 kim c) How does this driver's total 2 hrs 4 hrs 6 hrs distance compare to the original driver (the one that increased their speed gradually rather than suddenly jumping speeds)? This distance is closer to the actual distance the driver traveled