document.write( "Question 1006614: Please help me solve this problem: \r
\n" ); document.write( "\n" ); document.write( "An object is moving in a straight line from a fixed point. The displacement s (in meters) is given by s= -2t^2 + 28t + 45, t≥0 , where t is in seconds. \r
\n" ); document.write( "\n" ); document.write( "a) Find the velocity at any time.
\n" ); document.write( "b) What is the velocity at t=3s?
\n" ); document.write( "c) Find t when the object reaches its maximum displacement.
\n" ); document.write( "d) Find the maximum displacement reached by this object.
\n" ); document.write( "e) Determine the acceleration at any time.
\n" ); document.write( "d) Describe the direction of the motion at, t=3s, t=7s, and t=9s.
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Algebra.Com's Answer #622734 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "An object is moving in a straight line from a fixed point. The displacement s (in meters) is given by s= -2t^2 + 28t + 45, t≥0 , where t is in seconds. \r
\n" ); document.write( "\n" ); document.write( "a) Find the velocity at any time.
\n" ); document.write( "b) What is the velocity at t=3s?
\n" ); document.write( "c) Find t when the object reaches its maximum displacement.
\n" ); document.write( "d) Find the maximum displacement reached by this object.
\n" ); document.write( "e) Determine the acceleration at any time.
\n" ); document.write( "d) Describe the direction of the motion at, t=3s, t=7s, and t=9s.
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document.write( "a) Velocity is the derivative  = -4t + 28 .\r\n" );
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document.write( "b) Velocity at t=3s is v = (-4)*3 + 28 = -12 + 28 = 16 .\r\n" );
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document.write( "c) It is the time moment when the speed is zero: -4t + 28 = 0 -----> t =  = 7 sec. It is the same time moment when  = 0.\r\n" );
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document.write( "d) The maximum displacement reached by this object is s at t = 7 sec. Substitute t = 7 into s= -2t^2 + 28t + 45 to get s = 143 m.\r\n" );
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document.write( "e) Acceleration is the second derivative of s or the derivative of the velocity a = -2 .\r\n" );
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document.write( "f) At t=3s the body moves to \"positive s\". At t=7s the speed is zero. At t=9s the body moves to \"negative s\".\r\n" );
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