Kinematics formulas
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Translation: the change of position vector: ∆𝒙 = 𝒙𝒇𝒊𝒏𝒂𝒍 − 𝒙𝒊𝒏𝒊𝒕𝒊𝒂𝒍
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Velocity: the rate of change of translation: 𝒗=∆𝒙
=
∆𝑡
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Acceleration: the rate of change of velocity 𝒂=∆𝒗
=
∆𝑡
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Trajectory under constant velocity 𝒙(𝑡) = 𝒙𝑖𝑛𝑖𝑡𝑖𝑎𝑙 + 𝒗 𝑡
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Trajectory under constant acceleration
𝒙𝑓𝑖𝑛 −𝒙𝑖𝑛
𝑡𝑓𝑖𝑛 −𝑡𝑖𝑛
𝒗𝑓𝑖𝑛 −𝒗𝑖𝑛
𝑡𝑓𝑖𝑛 −𝑡𝑖𝑛
1
𝒙(𝑡) = 𝒙𝑖𝑛𝑖𝑡𝑖𝑎𝑙 + 𝒗𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑡 + 2𝒂 𝒕𝟐
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How to find a trajectory in more than one dimension: solving separately for each axis.
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http://physics.bu.edu/~duffy/HTML5/2Dmotion_race.html