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Understanding Linear Motion Equations: Displacement and Frame of Reference

This guide by Jessica Hall provides a comprehensive overview of the equations governing linear motion. It covers essential concepts such as displacement (∆x), time of travel (∆t), acceleration (a), and both initial (vi) and final velocity (vf). Key equations include Vf = Vi + at, ∆x = (Vi + Vf)t/2, and their derivations. The document elaborates on how these variables interrelate in linear motion, making it an excellent resource for students looking to grasp fundamental physics concepts in kinematics.

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Understanding Linear Motion Equations: Displacement and Frame of Reference

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  1. Linear Motion Equations By Jessica Hall Period 2

  2. Displacement- Frame of Reference ∆x = f-i ∆x=f-i :-10-0 = -10 :10-0=0 f= -10 i=0

  3. Variables for Linear Motion • d = displacement (∆x) • t = time of travel (∆t) • a = rate of constant acceleration • vi = initial velocity • vf = final velocity

  4. Equation 1 • ā = ∆v / ∆t = (Vf-Vi)/(Tf-Ti); • a/1=(Vf-Vi)/t; • at=Vf-Vi; • atVvi=Vf; • Vf=Vi+at(equation # 1)

  5. Equation 2 • v = ∆x/ ∆t; • ∆x=d, ∆t=t, V =1/2(vi+vf); • ½(Vi+Vf)=d/t; • t/2(Vi+Vf)=d or ½((Vi+Vf)t (equation # 2).

  6. Equation 3 Vf=Vi+at #1 into ½((Vi+Vf)t d = ½(Vi + at + Vi)td = ½(2Vi + at)t d = (Vi + ½at)t (equation # 3)

  7. Equation 4 • Vf= Vi +at; • Vf-Vi=at; • (Vf-Vi)/a=t. (i) • D=1/2(Vi+Vf)/[(Vf-Vi)/a]; • D=[(Vi+Vf)(Vf-Vi)]2a; • D=(VfVi+Vf^2-Vi^2VfVi)/2a • D=(Vf^2-Vi^2)/2a • 2ad=Vf^2-Vi^2 • Vf^2=2ad+Vi^2 (equation # 4).

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