# Linear Motion Equations ```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
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i
i
f
Vf = vi + at
Equation 2
 v = ∆x/ ∆t
v = &frac12;(v +v ) ∆x = d ∆t = t
i
f
=&frac12;(vi + vf) = d/t
&frac12;(vi + vf)t = d
d = &frac12;(vf + vi)t
Equation 3
d = &frac12;(v + at + v )t
d = &frac12;(2v + at)t
d = (v + &frac12;at)t
i
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i
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D = vi t + &frac12;at&sup2;
Equation 4
 vf = vi + at
-v
v – v = at
a
a
t=v –v
a
i
f
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f
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d = &frac12; (vf +vi) (vf – vi/a)
D = (vf + vi)(vf – vi)
a