Algebra.Com's Answer #814470 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A particle moving in a constant deceleration passes by two ports, which are 500 m apart, with velocity 40m/s and 20 m/s respectively.
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document.write( "Find the: (a) deceleration of the particle; (b) time after passing by the second post when it comes to rest
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document.write( " It can be solved as an Algebra problem, OR as a Calculus problem OR as a Physics problem.\r
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document.write( " The Physics solution is much more elegant and much more educative, so I will present here the Physics solution.\r
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document.write( "Let \"m\" be the mass of the particle; \"a\" be the constant deceleration.\r\n" );
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document.write( "Then the change of the kinetic energy between the ports is\r\n" );
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document.write( "  -  joules.\r\n" );
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document.write( "The deceleration force, acting on the particle, is the product ma, and the work of this force on the distance \r\n" );
document.write( "between the ports is ma*500 joules.\r\n" );
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document.write( "So, we can write the conservation energy equation in the form\r\n" );
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document.write( " - = 500ma\r\n" );
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document.write( "(change of the kinetic energy is equal to the work done).\r\n" );
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document.write( "Cancel the mass m in both parts of the equation; then substitute the given velocities. You will get\r\n" );
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document.write( "  -  = 500a.\r\n" );
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document.write( "Simplify and find deceleration value\r\n" );
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document.write( "  -  = 500a\r\n" );
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document.write( " 800 - 200 = 500a ---> 600 = 500a ---> a = 600/500 = 1.2.\r\n" );
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document.write( "Thus deceleration is 1.2 m/s^2. It is the answer to question (a).\r\n" );
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document.write( "After passing the second port, the particle will be at rest in 20/a = 20/1.2 = 16 2/3 seconds. It is the answer to question (b).\r\n" );
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document.write( "Solved.\r
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