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

Explanation

Projected vertically : Let us consider an object of mass m thrown vertically upwards with an initial velocity u. The air friction isneglected . In this case we select the vertical direction as positive y - axis as shown in the figure, then the acceleration a = - g.
g points towards the negative y - axis. The kinematic equations for this motion are
The velocity and position of the object at any time t are,
v = u - gt
s = `ut -(1)/(2) g t^(2)`
The velocity of the object at any position y is
`v^(2) = u^(2) - 2 gy`