MT 1810 Calculus II Course Activity I.7: Velocity and Distance Travelled
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1 MT 1810 Calculus II, CA I.7 P a g e 1 MT 1810 Calculus II Course Activity I.7: Velocity and Distance Travelled Name: Purpose: To investigate how to calculate the distance travelled by an object if you know the velocity of that object. Procedure: Work on the following activity with 1-2 other students during class (but be sure to complete your own copy) and finish the exploration outside of class. 1. Suppose on a recent car trip your velocity (in miles per hour) was given by the function , where is measured in hours. Your trip lasted from 0 to 3 hours. Estimate the total distance travelled by you on this trip. Use the following questions to help you with your estimate. What simplifying assumption would help you make an approximation? What are the units of? What are the units of distance travelled? Can you improve on your current estimate? How?
2 MT 1810 Calculus II, CA I.7 P a g e 2 2. Write a mathematical expression that represents the exact distance travelled on this trip. 3. Calculate the exact distance traveled using your answer to (2) and Mathematica. How close was your estimate? In the following questions use Mathematica to calculate exact answers where necessary. 4. A woman goes for her daily walk on a straight trail she always begins her walk at the beginning of the trail. Her velocity, (in miles per hour), on a particular day is given by the following function: 4,0 15 3,15 30 where is measured in minutes. a. What was the total distance that the woman walked on that day? b. How far was she from the beginning of the trail at the end of her walk?
3 MT 1810 Calculus II, CA I.7 P a g e 3 5. A particle moving along a straight line has a velocity, (in cm/sec), given by the following function: 9 5 sin where is measured in seconds. a. In total, how far does the particle travel between 0 and 3 seconds? b. In total, how far does the particle travel between 0 and 5 seconds? c. How far is the particle from where it started after 5 seconds?
4 MT 1810 Calculus II, CA I.7 P a g e 4 6. The following graph shows the velocity, (measured in miles per minute), of a car observed on a straight road from 0 to 5 minutes. The area between the curve and the axis in each segment is marked a. After 5 minutes, how far was the car from its position at 0 minutes? b. Write a description of a scenario that would explain this velocity graph extra points for the most entertaining story that is also correct!
5 MT 1810 Calculus II, CA I.7 P a g e 5 Class Discussion: What Have We Learned/Recalled in this Activity? Skills/Facts: Methods: Concepts to Understand:
6 MT 1810 Calculus II, CA I.7 P a g e 6 Methods Practice: Complete the following question individually. 1. Suppose a boat s velocity (in miles per hour) was given by the function 5e sin 1, where is measured in hours. The boat travels from 0 to 5 hours. a. Estimate the total distance travelled by the boat on this trip. (This should truly be an estimate do not use Mathematica to calculate an exact answer at this point in the question.) Use the following questions to help you with your estimate. What simplifying assumption would help you make an approximation? What are the units of? What are the units of distance travelled? Can you improve on your current estimate? How? b. Write a mathematical expression that represents the exact distance travelled on this trip. c. Calculate the exact distance traveled using your answer to (2) and Mathematica. How close was your estimate?
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