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File0031 - Section 3.3 The Derivative as a Rate of Change...

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Unformatted text preview: Section 3.3 The Derivative as a Rate of Change 115 16. (a) P is moving to the left when 2 < t < 3 or 5 < t < 6; P is moving to the right when 0 < t < 1; P is standing stillwhenl<t<20r3<t<5 (b) v (cm/sec) speed (cm/sec) velocity 17. (a) 190 ft/sec (b) 2 sec (c) at 8 sec, 0 ft/sec (d) 10.8 sec, 90 ft/sec (e) From t : 8 until t : 10.8 sec, a total of 2.8 sec (f) Greatest acceleration happens 2 sec after launch (g) Fromt = 2 to t = 10.8 sec; during this period, a : W m —32 ft/sec2 18. (a) Forward: Ogt<1and5 <t<7;Backward:1<t< 5;Speedsup:1<t<2and5 <t<6; Slowsdown: O£t< 1,3 <t< 5,and6<t< 7 (b) Positive: 3 <t< 6; negative: 0§t<2and6<t< 7; zero: 2<t< 3and7 <t< 9 (c) t=0and2§t§3 ”‘~ ((1) 7 S l S 9 19.5 : 49Ot2 => v = 980t fi a z 980 (a) Solving 160 : 490t2 "-> t: ‘73 sec. The average velocity was flag : 280 cm/sec. (b) At the 160 cm mark the balls are falling at v(4/7) 2 560 cm/sec. The acceleration at the 160 cm mark was 980 cm/secz. (c) The light was flashing at a rate of % : 29.75 flashes per second. 20. (a) ...
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