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𝑣 =
∆𝑥
∆𝑡
 
 
𝑣𝑚 =
∆𝑥
∆𝑡
 
𝑣 = 𝑥′ 
𝑎 = 𝑣′ = 𝑥′′ 
𝑎𝑚 =
∆𝑣
∆𝑡
 
𝑥 = 𝑥0 + 𝑣0𝑡 +
𝑎𝑡2
2
 
∆𝑥 = 𝑣0𝑡 +
𝑎𝑡2
2
 
𝑣 = 𝑣0 + 𝑎𝑡 
𝑣2 = 𝑣𝑜
2 + 2𝑎∆𝑥 
∆𝑥
∆𝑡
=
𝑣0 + 𝑣
2
 
 
 
 
 
 
𝑦 = 𝑦0 +
𝑔𝑡2
2
 
∆𝑦 =
𝑔𝑡2
2
 
𝑣 = 𝑔𝑡 
𝑣2 = 2𝑔∆𝑦 
∆𝑦
∆𝑡
=
𝑣
2
 
 
𝑦 = 𝑦0 + 𝑣0𝑡 −
𝑔𝑡2
2
 
∆𝑦 = 𝑣0𝑡 −
𝑔𝑡2
2
 
𝑣 = 𝑣0 − 𝑔𝑡 
𝑣2 = 𝑣𝑜
2 − 2𝑔∆𝑦 
∆𝑦
∆𝑡
=
𝑣0 + 𝑣
2
 
 
 
 
 
 
𝑟 = 𝑥𝑖̂ + 𝑦𝑗̂ + 𝑧�̂� 
∆𝑟⃗⃗⃗⃗⃗ = ∆𝑥𝑖̂ + ∆𝑦𝑗̂ + ∆𝑧�̂� 
𝑣𝑚⃗⃗⃗⃗⃗⃗ =
∆𝑟⃗⃗⃗⃗⃗
∆𝑡
=
∆𝑥
∆𝑡
𝑖̂ +
∆𝑦
∆𝑡
𝑗̂ +
∆𝑧
∆𝑡
�̂� 
𝑣 = 𝑣𝑥𝑖̂ + 𝑣𝑦𝑗̂ + 𝑣𝑧�̂� = 𝑥
′𝑖̂ + 𝑦′𝑗̂ + 𝑧′�̂� 
𝑎𝑚⃗⃗ ⃗⃗⃗⃗ =
∆𝑣⃗⃗ ⃗⃗ ⃗
∆𝑡
=
∆𝑣𝑥
∆𝑡
𝑖̂ +
∆𝑣𝑦
∆𝑡
𝑗̂ +
∆𝑣𝑧
∆𝑡
�̂� 
�⃗� = 𝑎𝑥𝑖̂ + 𝑎𝑦𝑗̂ + 𝑎𝑧�̂� = 𝑣𝑥
′𝑖̂ + 𝑣𝑦
′𝑗̂ + 𝑣𝑧
′�̂� 
|�⃗⃗�| = √𝑉𝑥
2 + 𝑉𝑦
2 + 𝑉𝑧
2 
𝜃 = tan−1
𝑉𝑧
√𝑉𝑥
2 + 𝑉𝑦
2
 
 
𝑟 = (𝑥0 + 𝑣0 cos𝜃0 𝑡)𝑖̂ + (𝑦0 + 𝑣0 sin 𝜃0 𝑡 −
𝑔𝑡2
2
) 𝑗̂ 
∆𝑟⃗⃗⃗⃗⃗ = (𝑣0 cos 𝜃0 𝑡)𝑖̂ + (𝑣0 sin 𝜃0 𝑡 −
𝑔𝑡2
2
) 𝑗̂ 
𝑣 = 𝑥′𝑖̂ + 𝑦′𝑗̂ = (𝑣0 cos𝜃0)𝑖̂ + (𝑣0 sin 𝜃0 − 𝑔𝑡)𝑗 ̂
�⃗� = (−𝑔)𝑗̂ 
 
𝑣 = −
𝑣𝑦
𝑟
𝑖̂ +
𝑣𝑥
𝑟
𝑗̂ 
�⃗� = −
𝑣2𝑥
𝑟2
𝑖̂ −
𝑣2𝑦
𝑟2
𝑗̂ 
𝑎𝑐𝑝 =
𝑣2
𝑟
 
𝑇 =
∆𝑡
𝑛
 𝑓 =
𝑛
∆𝑡
 
𝑣 =
2𝜋𝑟
𝑇
 𝑣 = 2𝜋𝑟𝑓 𝜔 = 2𝜋𝑓 
 
∑�⃗� = 𝑚�⃗� 
�⃗⃗� = 𝑚�⃗� 
𝐹𝐺 =
𝐺𝑀𝑚
𝑟2
 
�⃗� =
∑ �⃗�
𝑚
=
∑𝐹𝑥⃗⃗⃗⃗
𝑚
𝑖̂ +
∑𝐹𝑦⃗⃗ ⃗⃗
𝑚
𝑗̂ +
∑𝐹𝑧⃗⃗⃗⃗
𝑚
�̂� 
 
𝑁 = 𝑃 
𝑁 = 𝑃 − 𝑚𝑎 
𝑁 = 𝑃 + 𝑚𝑎 
𝑁 = 𝑃 cos𝜃

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