Kinematic Equations
“suvat” equations
Kinematic Equations
“suvat” equations
Motion with Uniform Acceleration
“suvat” Equation #1
Finding final velocity
• Start with 𝑎 =
𝑣−𝑢
𝑡
• Rearrange and solve for v
• 𝑣 = 𝑢 + 𝑎𝑡
• Displacement (s) does not appear in this equation
Kinematic Equations
“suvat” equations
• Only work when acceleration is uniform (constant)!!
• Mathematical relationships between:
•
•
•
•
•
displacement (s)
initial velocity (u)
final velocity (v)
acceleration (a)
time (t)
“suvat” Equation #1
Finding final velocity
All equations
derived from three
relationships that
are already
known
• 𝑣𝑎𝑣𝑔 =
•𝑎=
∆𝑣
𝑡
• 𝑣𝑎𝑣𝑔 =
𝑠
𝑡
𝑜𝑟 𝑎 =
𝑢+𝑣
𝑣−𝑢
𝑡
2
“suvat” Equation #1
Finding final velocity
• To confirm this:
• 𝑠𝑙𝑜𝑝𝑒 =
•𝑎=
𝑣−𝑢
∆𝑦
∆𝑥
• Or, from slope-intercept form
• 𝑦 = 𝑚𝑥 + 𝑏
• 𝑣 = 𝑎𝑡 + 𝑢
𝑡
• Rearranging:
• 𝑣 = 𝑢 + 𝑎𝑡
1
“suvat” Equation #2
Finding displacement
“suvat” Equation #3
Finding final velocity
• Finidng area under a velocity
graph gives displacement
• 𝑠 = 𝐴𝑟𝑒𝑐𝑡 + 𝐴𝑡𝑟𝑖
• 𝑠 = 𝑢×𝑡 +
1
2
• The first two equations both
contain “t”
• Rearranging the first equation to
isolate “t”
• Substitute expression for “t”
into second equation and
simplify
• Time (t) does not appear in this
equation
𝑡× 𝑣−𝑢
• 𝑠 = 𝑢𝑡 + 12𝑎𝑡2
• Final velocity (v) does not
appear in this equation
“suvat” Equations
Equation
“suvat” equation #4
Finding displacement
• 𝑠 = 𝑢𝑡 + 12𝑎𝑡2
•𝑡=
𝑣−𝑢
𝑎
• 𝑣2 = 𝑢2 + 2𝑎𝑠
• Start with the two equations for
“vavg”
• Set them equal to one another:
• Rearrange:
• 𝑣𝑎𝑣𝑔 =
• 𝑣𝑎𝑣𝑔 =
𝑠
𝑢+𝑣
𝑡
2
• =
•𝑠=
𝑠
𝑡
𝑢+𝑣
𝑢+𝑣
2
2
t
Solving Problems Using “suvat” Equations
s
𝑣 = 𝑢 + 𝑎𝑡
u
v
a
t
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𝑠 = 𝑢𝑡 + 12𝑎𝑡 2
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𝑣 2 = 𝑢 2 + 2𝑎𝑠

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𝑣+𝑢
𝑠=
𝑡
2
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• Determine what the question is asking for
• List all known quantities
• Remember, each equation contains four variables, so you need to know
three variables in order to solve for the fourth
• Pick the appropriate equation
• Solve for desired quantity
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2