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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