By Rachael Jefferson

Acceleration is the rate of change in velocity with respect to time. A avg = ∆v/∆t = (v f -v i )/(t f -t i ) 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.

d = displacement (∆x) t = time of travel (∆t) a = rate of constant acceleration v i = initial velocity v f = final velocity

V avg = ∆x/ ∆tv = ∆x/ ∆t A avg = ∆v/ ∆tā = ∆v/ ∆t

ā = ∆v / ∆t ā = a ∆v = v f – v i ∆t = t A = v f – v i at = v f - v i t +vi + v i at + v i = v f V f = v i + at

v = ∆x/ ∆t v = ½(v i +v f ) ∆x = d ∆t = t =½(v i + v f ) = d/t ½(v i + v f )t = d d = ½(vf + vi)t

d = ½(v i + at + v i )t d = ½(2v i + at)t d = (v i + ½at)t D = v i t + ½at²

v f = v i + at -v i v f – v i = at a a t = v f – v i a d = ½ (vf +vi) (vf – vi/a) D = (vf + vi)(vf – vi) a 2ad = (vf + vi)(vf-vi) = v f ² - v f v i + v f v i – v i ² 2ad = v f ² - v i ² +v i ² v i ² + 2ad = v f ² vf² = vi² + 2ad