Kinematic Equations
Describe Motion of an Objectball, rocket, person…
• Used in situations with
uniform acceleration
a
=+
o
vv
α
t
Equation #1 (velocity)
at
t
0
average
v+
v
v = v
=
2
0
v
x
v =
=
2
t
∆
0
v
=
2
x
t
∆
2
00
0
v +
1
=
v
22
at
tta
t
Kinematic Equations—12
Constant Acceleration
Eq. 1
=
+
o
vv a
t
∆=
+
2
1
2
o
xv
t a
t
or
0
v  v
t=
a
Eq. 2
=
+∆
2
o
a
x
Eq. 3
Putting t from Eq. 1
into Eq. 2 we get
Eq.3
 and 3
Note Eq. 3 is not independent of Eq. 1 and Eq. 2
ProblemSolving Hints
• Read the problem
• Draw a diagram
– Choose a coordinate system, label initial and final points, indicate
a positive direction for velocities and accelerations
• Label all quantities, be sure all the units are consistent
– Convert if necessary
• Choose the appropriate kinematic equation
• Solve for the unknowns
– You may have to solve two equations for two unknowns
• Check your results
– Estimate and compare
– Check units
Free Fall
• All objects moving under the influence of
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 Spring '06
 Buchler
 Physics, Addition, Acceleration, Velocity, ax

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