Summary Table of formulas

ALL THE FORMULAS!
Physics 1- first semester data analysis

, 𝚫𝒙 ≡ 𝒙𝒇 − 𝒙𝒊 Displacement
𝚫𝒙
̅ ≡
𝒗 Average velocity
𝚫𝒕
𝒕𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
Average speed
𝒕𝒐𝒕𝒂𝒍 𝒕𝒊𝒎𝒆
𝚫𝒙 𝒅𝒙
𝒗𝒙 ≡ 𝐥𝐢𝐦 = Instantaneous velocity
𝚫𝒕 →𝟎 𝚫𝒕 𝒅𝒕
𝒔𝒙 = |𝒗𝒙 | Instantaneous speed
𝚫𝒗𝒙 𝒗𝒙𝒇 − 𝒗𝒙𝒊
𝒂𝒙 ≡
𝚫𝒕
=
𝒕𝒇 − 𝒕𝒊
Average acceleration
𝚫𝒗𝒙 𝒅𝒗𝒙
𝒂𝒙 ≡ 𝐥𝐢𝐦 = Instantaneous acceleration
𝚫𝒕 →𝟎 𝚫𝒕 𝒅𝒕
𝒗𝒙𝒇 = 𝒗𝒙𝒊 + 𝒂𝒙 𝒕 Velocity as a function of time
𝒗𝟐𝒙𝒇 = 𝒗𝟐𝒙𝒊 + 𝟐𝒂𝒙 (𝒙𝒇 − 𝒙𝒊 ) Velocity as a function of position
𝟏
𝒙𝒇 = 𝒙𝒊 + (𝒗 + 𝒗𝒙𝒇 )𝒕 Position as a function of velocity and time
𝟐 𝒙𝒊
𝟏
𝒙𝒇 = 𝒙𝒊 + 𝒗𝒙𝒊 𝒕 + 𝒂𝒙 𝒕𝟐 Position as a function of time
𝟐
𝟏
𝒙 = 𝒈𝒕𝟐 Position of a freely falling object
𝟐
𝒗 = 𝒈𝒕 Velocity of a freely falling object