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By Rachael Jefferson Acceleration Acceleration is the rate of change in velocity with respect to time. Aavg = ∆v/∆t = (v -v )/(t -t ) 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. f i f i Variables for Linear Motion d = displacement (∆x) t = time of travel (∆t) a = rate of constant acceleration vi = initial velocity vf = final velocity Definitions of linear motion Vavg = ∆x/ ∆t Aavg = ∆v/ ∆t v = ∆x/ ∆t ā = ∆v/ ∆t Equation 1 ā = ∆v / ∆t ā = a ∆v = vf – vi ∆t = t A=v –v t f i at = v - v +vi + v at + v = v f i i i f Vf = vi + at Equation 2 v = ∆x/ ∆t v = ½(v +v ) ∆x = d ∆t = t i f =½(vi + vf) = d/t ½(vi + vf)t = d d = ½(vf + vi)t Equation 3 d = ½(v + at + v )t d = ½(2v + at)t d = (v + ½at)t i i i i D = vi t + ½at² Equation 4 vf = vi + at -v v – v = at a a t=v –v a i f i f i 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 vf² = vi² + 2ad