Linear Motion Equations

1. Linear Motion Equations By Rachael Jefferson

2. 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.

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. Definitions of linear motion • Vavg = ∆x/∆t v = ∆x/∆t • Aavg = ∆v/∆t ā = ∆v/∆t

5. Equation 1 • ā = ∆v / ∆tā = a ∆v = vf– vi ∆t = t A = vf – vi at = vf- vi t +vi+ vi at + vi = vf Vf = vi + at

6. Equation 2 • v = ∆x/∆t v = ½(vi+vf) ∆x = d ∆t = t =½(vi + vf) = d/t ½(vi + vf)t = d d = ½(vf + vi)t

7. Equation 3 d = ½(vi + at + vi)td = ½(2vi + at)t d = (vi + ½at)t D = vi t + ½at²

8. Equation 4 d = ½ (vf +vi) (vf – vi/a) D = (vf + vi)(vf – vi) a 2ad = (vf + vi)(vf-vi) = vf² - vfvi + vfvi – vi² 2ad = vf² - vi² +vi²+vi² vi² + 2ad = vf² • vf = vi + at -vi vf – vi = at a a t = vf – vi a vf² = vi² + 2ad