document.write( "Question 1143152: The distance, in feet, that a certain object travels after t seconds is given by the function d(t)=a(t)+1/2bt2, where a and b are positive constants. Which of the following functions,s, represents the average (arithmetic mean) rate in feet per second, when the object has traveled t seconds?\r
\n" ); document.write( "\n" ); document.write( "a) s(t)= 2t
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Algebra.Com's Answer #763927 by ikleyn(52771) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1.  Let me start explaining that the condition is written incorrectly.\r\n" );
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document.write( "    The correct formula for the distance traveled is  d(t) = a*t + (1/2)*bt^2.\r\n" );
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document.write( "    instead of  d(t) = a(t) + (1/2)*b*t^2.\r\n" );
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document.write( "    (Since \"a\" is a constant, there is no sense to write a(t), presenting \"a\" as a function of \"t\".)\r\n" );
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document.write( "2.  Let me continue, stating that the optional answer list  DOES NOT CONTAIN the correct formula (!)\r\n" );
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document.write( "        (In other words, no one of the proposed options does fit as the correct answer.)\r\n" );
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document.write( "3.  Let me to explain you what happens in reality, from the Physics point of view.\r\n" );
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document.write( "    The given distance formula presents the distance at the uniformly accelerated rectilinear move.\r\n" );
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document.write( "    \"a\" is the initial velocity.  \"b\" is the acceleration.\r\n" );
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document.write( "    At such move, the velocity  is the linear function of time  v(t) = a + b*t.\r\n" );
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document.write( "    The arithmetic mean of the rate  is   = . \r\n" );
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document.write( "    It is the correct answer.\r\n" );
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document.write( "    The average rate, calculated as the traveled distance divided by the time, is the same\r\n" );
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document.write( "          = .\r\n" );
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document.write( "4.  Final answer is  ,\r\n" );
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document.write( "    which is not in the list.\r\n" );
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