A Laurel Springs school bus is traveling on a straight stretch of highway. Information regarding the...

 

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A Laurel Springs school bus is traveling on a straight stretch of highway. Information regarding the bus's velocity and acceleration at various values of time are shown in the table. There are no discontinuities on the functions for v(t) and a(t). t (sec) 0 15 25 v(t) -20 -30 25 30 30 35 50 50 60 60 -20 -14 10010 (ft/sec) a(t) 1 5 2 1 2 4 2 (ft/sec) a. Explain the meaning of the integral 5000 lv(t)) dt in terms of the bus's motion and approximate this integral using a trapezoidal approximation over three intervals. Include units of measure in your discussion. b. Explain the meaning of the integral 30 a(t) dt in terms of the bus's motion; and find the exact value of this integral. Include units of measure in your discussion. C. For 0 < t < 60, must there be a time t when v(t) = -5? Provide justification for your answer. d. For 0 A Laurel Springs school bus is traveling on a straight stretch of highway. Information regarding the bus's velocity and acceleration at various values of time are shown in the table. There are no discontinuities on the functions for v(t) and a(t). t (sec) 0 15 25 v(t) -20 -30 25 30 30 35 50 50 60 60 -20 -14 10010 (ft/sec) a(t) 1 5 2 1 2 4 2 (ft/sec) a. Explain the meaning of the integral 5000 lv(t)) dt in terms of the bus's motion and approximate this integral using a trapezoidal approximation over three intervals. Include units of measure in your discussion. b. Explain the meaning of the integral 30 a(t) dt in terms of the bus's motion; and find the exact value of this integral. Include units of measure in your discussion. C. For 0 < t < 60, must there be a time t when v(t) = -5? Provide justification for your answer. d. For 0