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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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