document.write( "Question 1184351: Find the time it takes to travel 30km for a bus which accelerates uniformly from 40km/hr to 80km/hr. Show your solution. \n" ); document.write( "
Algebra.Com's Answer #814919 by ikleyn(52797)\"\" \"About 
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document.write( "You are given:  initial velocity  \"v%5B1%5D\" = 40 km/h;\r\n" );
document.write( "                ending  velocity  \"v%5B2%5D\" = 80 km/h;\r\n" );
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document.write( "                travel distance   d = 30 km.\r\n" );
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document.write( "To find the time, start from these two kinematic equations\r\n" );
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document.write( "    d = \"v%5B1%5D%2At\" + \"%28a%2At%5E2%29%2F2\",      (1)\r\n" );
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document.write( "    a = \"%28v%5B2%5D-v%5B1%5D%29%2Ft\",            (2)\r\n" );
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document.write( "where \" a \" is the acceleration.  Substitute (2) into (1), eliminating \"a\".  You will get\r\n" );
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document.write( "    d = \"v%5B1%5D%2At+%2B+%28%28v%5B2%5D-v%5B1%5D%29%2F%282t%29%29%2At%5E2\" = \"v%5B1%5D%2At+%2B+%28%28v%5B2%5D-v%5B1%5D%29%2F2%29%2At\" = \"v%5B1%5D%2At+%2B+%28v%5B2%5D%2At%29%2F2+-+%28v%5B1%5D%2At%29%2F2\" = \"%28v%5B1%5D%2At%29%2F2+%2B+%28v%5B2%5D%2At%29%2F2\" = \"%28%28v%5B1%5D%2Bv%5B2%5D%29%2F2%29%2At\".\r\n" );
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document.write( "Thus you started from the formal kinematic formula (1)  and ended with intuitively understandable formula\r\n" );
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document.write( "    d = \"%28%28v%5B1%5D%2Bv%5B2%5D%29%2F2%29%2At\".\r\n" );
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document.write( "Now you only need substitute the given data to get simple equation\r\n" );
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document.write( "    30 = \"%28%2840%2B80%29%2F2%29%2At\"\r\n" );
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document.write( "    30 = 60t\r\n" );
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document.write( "     t = \"30%2F60\" = \"1%2F2\"  of an hour = 30 minutes.    ANSWER\r\n" );
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