document.write( "Question 1204876: A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t) = (0.860 m/s^3)t^2. What is the acceleration of the car when vx = 12.0vm/s?\r
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Algebra.Com's Answer #841418 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A race car starts from rest and travels east along a straight and level track.
\n" ); document.write( "For the first 5.0 s of the car's motion, the eastward component of the car's velocity
\n" ); document.write( "is given by vx(t) = (0.860 m/s^3)t^2. What is the acceleration of the car when vx = $\"highlight%28cross%2812_0vm%2Fs%29%29\"$ 12.0 m/s ?
\n" ); document.write( "problem from Young and Freedman. University Physics with Modern Physics. Fifteenth Edition.
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\n" ); document.write( "\n" ); document.write( "        (1)   In your post, I fixed errors where I saw them. Instead of 12.0vm/s should be 12.0 m/s.\r
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\n" ); document.write( "\n" ); document.write( "       (2)   Everythere in the formulas, where you see lowercase letter x, it is, actually, subscript x.\r
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\n" ); document.write( "\n" ); document.write( "             It only designates x-component of the velocity.\r
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\n" ); document.write( "\n" ); document.write( "             It is strange that in this problem they abused writing x everywhere.
\n" ); document.write( "             It easily could be omitted, at all, since y-component ABSENTS in this problem.\r
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document.write( "                   Solution\r\n" );
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document.write( "For x-component of the car's velocity we have this expression\r\n" );
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document.write( "    (t) =      (1)   (given)\r\n" );
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document.write( "(distance in meters, time in seconds).  Notice that this movement is neither uniform nor uniformly accelerated.\r\n" );
document.write( "It is a movement with variable acceleration.\r\n" );
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document.write( "The acceleration of the car a(t) is the derivative of the speed function of time.\r\n" );
document.write( "So we write accordingly\r\n" );
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document.write( "            dv(t)                         \r\n" );
document.write( "     = -------,   or   a(t) =  (0.860*t^2)' = 2*0.860*t = 1.720*t.    (2)\r\n" );
document.write( "             dt                            \r\n" );
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document.write( "Next, we want to know at which time t  (t) = 12.0 m/s.\r\n" );
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document.write( "Using expression (1) for (t), we write\r\n" );
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document.write( "     = 12,   =  = 13.95348837,  t =  = 3.73544 s (rounded).\r\n" );
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document.write( "Notice that this time t = 3.73544 seconds is less than 5 seconds; so, according to the problem, all the formulas,\r\n" );
document.write( "which we used on the way, were valid.\r\n" );
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document.write( "Now we make the final step: to learn what is the acceleration of the car at the time moment 3.73544 seconds,\r\n" );
document.write( "we simply substitute t= 3.73544 into the formula (2) for acceleration, which we derived earlier.\r\n" );
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document.write( "It gives us  a(3.73544) = 1.720*3.73544 = 6.4249568 m/s^2.\r\n" );
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document.write( "You may round it in a way you need / (you want).\r\n" );
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document.write( "At this point, all separate pieces are connected together, and we have the\r\n" );
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document.write( "ANSWER.  When  = 12.0 m/s, the acceleration of the car is 6.4249568 m/s^2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is not an easy task to understand this interweaving and interaction of concepts and numbers.
\n" ); document.write( "To do this, you need to firmly know their meaning, definitions and interconnections.
\n" ); document.write( "Also, knowledge of Calculus is a MUST.\r
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\n" ); document.write( "\n" ); document.write( "I hope that my post will help you to navigate in this ocean.\r
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