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This Concept Map, created with IHMC CmapTools, has information related to: Kinematics, Solutions to differential equations a=dv/dt v=dx/dt where a is constant base equations <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> t+ </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> V= </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +at </mtext> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> ⇒ X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +Vt- </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </mrow> </math>, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) tools needed to apply Component Vectors, X X0 V V0 a t solutions If 4 of the 6 quantities are known, the other 2 can be found using the equations, Solutions to differential equations a=dv/dt v=dx/dt where a is constant base equations <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> V= </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +at </mtext> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> t+ </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </math> solutions If 4 of the 6 quantities are known, the other 2 can be found using the equations, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) tools needed to apply Coordinate Systems (unit vector notation), <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> V= </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +at </mtext> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate t ⇒ </mtext> <mmultiscripts> <mtext> V </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> <mtext> = </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <mtext> 2 </mtext> </mmultiscripts> <mtext> +2a(X- </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> ) </mtext> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> t+ </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> ⇒ X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +Vt- </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </mrow> </math>, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) tools needed to apply Vector Algebra, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) tools needed to apply Vectors, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) tools needed to apply Displacement, Velocity & Acceleration, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> t+ </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate t ⇒ </mtext> <mmultiscripts> <mtext> V </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> <mtext> = </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <mtext> 2 </mtext> </mmultiscripts> <mtext> +2a(X- </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> ) </mtext> </mrow> </math>, Solutions to differential equations a=dv/dt v=dx/dt where a is constant kinematic quantities X X0 V V0 a t, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> V= </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +at </mtext> </math> solutions If 4 of the 6 quantities are known, the other 2 can be found using the equations, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> t+ </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> a </mtext> <mmultiscripts> <mtext> t </mtext> <none/> <mtext> 2 </mtext> </mmultiscripts> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate a ⇒ X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> (V+ </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> )t </mtext> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> V= </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> +at </mtext> </math> algebraically combined <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> eliminate a ⇒ X= </mtext> <mmultiscripts> <mtext> X </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> + </mtext> <mfrac> <mtext> 1 </mtext> <mtext> 2 </mtext> </mfrac> <mtext> (V+ </mtext> <mmultiscripts> <mtext> V </mtext> <mtext> 0 </mtext> <none/> </mmultiscripts> <mtext> )t </mtext> </mrow> </math>, Kinematics (the analysis of motion) H&R Ch2,3,4 (18% of APC exam) derived Solutions to differential equations a=dv/dt v=dx/dt where a is constant