Answer:
First Equation: Vf = Vi – g t
Final velocity Vf = Initial velocity Vi + Acceleration x time
assume direction of Vi is opposite to direction of acceleration g
Vf = Vi – g t --------------------------------(1) First Equation of linear motion
Second Equation: Distance travelled S = Vi x t – ½ gt^2
Average velocity Va = ½ (Vi + Vf) = ½ (Vi + Vi - gt) = Vi - ½ gt
Distance travelled = Va x t = (Vi - ½ gt) x t = Vi x t – ½ gt^2
S = Vi x t – ½ gt^2---------------------------(2) Second equation of linear motion
Third Equation: Distance travelled 2gs = Vf^2 – Vi^2
From first equation t = (Vi – Vf)/g Substitute t into second equation
Distance travelled S = Vi x (Vi – Vf)/g - ½ g [(Vi – Vf)/g]^2 multiply both sides 2g
2gS = 2Vi^2 - 2ViVf - Vi^2 + 2 ViVf – Vf^2 simplify
2gS = Vf^2 – Vi^2 assume direction of Vi opposite to g
2gS = Vf^2 – Vi^2 ---------------------------(3) Third equation of linear motion
I hope this helps.
Shailesh (Sky) Kadakia, Former Professor
University of Pittsburgh, Johnstown PA
Expert Math and Physics tutor with WYZANT
