Exercises 51 time velocity time velocity min m sec

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Exercises 5.1 Time Velocity Time Velocity (min) (m , sec) (min) (m , sec) 0 1 35 1.2 5 1.2 40 1.0 10 1.7 45 1.8 15 2.0 50 1.5 20 1.8 55 1.2 25 1.6 60 0 30 1.4     Time Velocity Time Velocity (sec) (in. , sec) (sec) (in. , sec) 0 0 6 1 12 7 2 22 8 3 10 9 4 5 10 5 13 11 6 2 6 0     10. Distance traveled upstream You are sitting on the bank of a tidal river watching the incoming tide carry a bottle upstream. You record the velocity of the flow every 5 minutes for an hour, with the results shown in the accompanying table. About how far upstream did the bottle travel during that hour? Find an estimate using 12 subintervals of length 5 with a. left-endpoint values. b. right-endpoint values. The choices for the c k could maximize or minimize the value of ƒ in the k th subinterval, or give some value in between. The true value lies somewhere between the approximations given by upper sums and lower sums. The finite sum approximations we looked at improved as we took more subintervals of thinner width. Velocity Velocity Time (converted to ft , sec) Time (converted to ft , sec) (sec) (30 mi , h = 44 ft , sec) (sec) (30 mi , h = 44 ft , sec) 0 0 70 15 10 44 80 22 20 15 90 35 30 35 100 44 40 30 110 30 50 44 120 35 60 35     12. Distance from velocity data The accompanying table gives data for the velocity of a vintage sports car accelerating from 0 to 142 mi > h in 36 sec (10 thousandths of an hour). Time Velocity Time Velocity (h) (mi , h) (h) (mi , h) 0.0 0 0.006 116 0.001 40 0.007 125 0.002 62 0.008 132 0.003 82 0.009 137 0.004 96 0.010 142 0.005 108    
308 Chapter 5: Integrals hours 0

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