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document.write( "The velocity function(in meters per second) for a particle moving along a line is given by v(t)=cos(t).
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document.write( "a. Graph the velocity from t=0 to t=2pi
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document.write( "B. Find the displacement of the particle from t=0 to t=pi
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document.write( "C. Find the total distance traveled by the particle from t=0 to t=pi
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document.write( "(a) To make a plot, go to website www.desmos.co./calculator\r\n" );
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document.write( " Find there an online plotting tool, free of charge for common use.\r\n" );
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document.write( " Print your given function for velocity and get the plot immediately.\r\n" );
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document.write( "(b) The displacement of the particle from t= 0 to t = 
is the integral\r\n" );
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document.write( " from 0 to of the velocity, which is cos(t).\r\n" );
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document.write( " Function cos(t) is zero at t= 
and is odd-symmetric about this point t= .\r\n" );
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document.write( " It implies that the integral of cos(t) from 0 to equals to 0 (zero).\r\n" );
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document.write( " Thus the displacement under the question (b) is zero.\r\n" );
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document.write( " It means that at t= the particle returns to the initial point.\r\n" );
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document.write( "(c) The total distance traveled by the particle from t= 0 to t = is the integral\r\n" );
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document.write( " from 0 to of function |cos(t)| (notice the absolute value sign).\r\n" );
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document.write( " Function cos(t) is zero at t= and is odd-symmetric about this point t= .\r\n" );
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document.write( " It implies that function |cos(t)| is an EVEN function about the point t= .\r\n" );
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document.write( " Hence, integral of |cos(t)| from 0 to equals to doubled integral of function cos(t) \r\n" );
document.write( " from 0 (zero) to .\r\n" );
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document.write( " Integral of function cos(t) from 0 (zero) to is 1-0 = 1.\r\n" );
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document.write( " //Notice that anti-derivative for cos(t) is sin(t). //\r\n" );
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document.write( " Thus the total distance traveled by the particle under question (c) is 2*1 = 2 units.\r\n" );
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document.write( "Solved.\r
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document.write( "This problem teaches you to distinct between notions/conceptions \"displacement\" and \"total traveled distance\".\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
