Linear Motion Equations

1. Linear Motion Equations By Abdul Khan Period 2

2. Displacement Change in position; Can be positive or negative, depending on direction; ∆x = Xf – Xi change in position equals final position minus initial position; Displacement and distance traveled are not the same thing;

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

4. Velocity Average Velocity = Change in position/change in direction; V-avg = ∆x/ ∆t = (xf-xi)/(tf-ti); Velocity is not the same as speed, velocity has direction; Average velocity and instantaneous velocity are not the same thing either.

5. Graphing Velocity Put time on the x-axis; Put displacement on the y-axis; The slope of the line is ∆x/ ∆t so the slope is velocity: x ∆x ∆t y

6. Acceleration Acceleration is the rate of change in velocity with respect to time Aavg= ∆v/∆t = (vf-vi)/(tf-ti) Notice how this form looks similar to that of velocity (∆x/∆t) Just as the slope of x vs. t is velocity, the slope of v vs. t is acceleration.

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

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

9. 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).

10. 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)

11. 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).