Rate of Change: Rollercoaster

Rate of Change: Rollercoaster
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  • Susan is at the amusement park with her two kids Bob and Jason. Bob just ate a hot dog and Jason hasn't been feeling well.
  • Mom I don't feel so well either!
  • Jason
  • Susan
  • Oh man! I think I ate too much! I might feel sick if we go on the rollercoaster now
  • Bob
  • Whatever works, I just do not want to get nauseous!
  • Don't worry kids, only a certain speed will get you nauseous on the rollercoaster. Rollercoasters are fastest during their first drop.
  • Mom you are right. We can use math to help us!
  • So the first drop of the rollercoaster takes place in the time interval between 10 seconds and 20 seconds
  • I guess math is helpful!
  • So if the average speed between that time interval is greater than 4 m/s, it will be too fast for me to handle and I won't be able to ride the rollercoaster.
  • Yes, if the instantaneous speed of the roller coaster at exactly 16 seconds is higher than 3m/s then Jason cannot ride this rollercoaster
  • Wow! I didn't realize we can use math in the real world!
  • Jason, you should be looking at the instantaneous speed of the rollercoaster!
  • So can we ride the rollercoaster or not. Use rates of change for an accurate answer!
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