Algebra.Com's Answer #787384 by ikleyn(52797)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The position function of a moving object is  .\r
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document.write( "a. When t = 2, what is the position of the object?
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document.write( "b. Determine the velocity function v(t).
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document.write( "c. For what valid values of t has the object stopped?
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document.write( "d. Determine the intervals when the object is moving east and moving west for valid values of t.
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document.write( "e. Is the object moving away or toward the origin at t = 2 s?
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document.write( "f. What is the acceleration function a(t)?
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document.write( "g. At t = 2 is the object speeding up or slowing down?
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document.write( "h. Determine the total distance travelled in the first 5 seconds.
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document.write( "(a) It is s(2). Substitute t= 2 into the formula and calculate.\r\n" );
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document.write( " I will not calculate it for you. It is YOUR job.\r\n" );
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document.write( "(b) To get the velocity function v(t), differentiate the given position function over t.\r\n" );
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document.write( " I will not differentiate it for you - it is YOUR job.\r\n" );
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document.write( "(c) These values of t are those where the velocity function is zero.\r\n" );
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document.write( " In other words, you need to solve the equation v(t) = s'(t) = 0.\r\n" );
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document.write( " This equation is formally of the third degree, but it can be factored and reduced to the lower degrees equations.\r\n" );
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document.write( "(d) The object is moving east if (and where) v(t) > 0.\r\n" );
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document.write( " The object is moving west if (and where) v(t) < 0.\r\n" );
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document.write( "(e) Calculate s(2) and v(2). \r\n" );
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document.write( " If s(2) < 0 and v(2) > 0, the object moves toward the origin.\r\n" );
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document.write( " If s(2) > 0 and v(2) < 0, the object moves toward the origin.\r\n" );
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document.write( " Otherwize, it moves away from the origin.\r\n" );
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document.write( "(f) Acceleration a(t) is the SECOND derivative of the position function over t.\r\n" );
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document.write( "(g) If v(2) > 0 and a(2) > 0, then the object is speeding (in the East direction).\r\n" );
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document.write( " If v(2) > 0 and a(2) < 0, then the object is slowing down.\r\n" );
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document.write( " If v(2) < 0 and a(2) > 0, then the object is slowing down.\r\n" );
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document.write( " If v(t) < 0 and a(t) < 0, then the object is speeding (but in the West direction).\r\n" );
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document.write( "Working on this assignment, my goal was to teach you.\r
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document.write( "It was not to work instead of you or to do your job.\r
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document.write( "Do not forget to post your \"THANKS\" for my teaching.\r
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document.write( "If you still have questions, do not hesitate to post them to me.\r
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document.write( "Happy learning (!)\r
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