Derive the equations of motion for a particle (a) falling vertically (b) projected vertically.

Explanation

Case (b) :
(i) Consider an object of mass 'm' thrown vertically upward with an initial velocity u.
(ii) Assume that there is no air resistance and acceleration due to gravity is constant near surface of the Earth.
(iii) the final velocity and displacement at any time 't' is v and y respectively. Further acceleration a is equal to `-g`.
(iv) Therefore equations of motion are,
`v=u-g t`
`y=ut-(1)/(2) g t^(2)`
`v^(2)=u^(2)-2gy`