Free-fall : Discuss the motion of an object under free fall. Neglect air resistance.

Explanation

An object released near the surface of the earth is accelerated downward under the influence of the force of gravity. The magnitude of acceleration due to gravity is represented by g. If air resistance is neglected, the object is said to be in free fall. If the height through which the object falls is small compared to the earth's radius, g can be taken to be constant, equal to `9.8 ms^(-2)`. Free fall is thus a case of motion with uniform acceleration.
We assume that the motion is in y-direction. more correctly in -y-direction because we choose upward direction as positive. Since the acceleration due to gravity is always downward, it is in the negative direction and we have
`a = - g = - 9.8 ms^(-2)`
the object is released from rest at `y = 0`. Therefore, `v_(0) = 0` and the equations of motion becomes:
`v = 0 - g t" " = - 9.8 t " " ms^(-1)`
`y = 0 - 1//2 g t^(2) " " = - 4.9 t^(2) " " m`
`v^(2) = 0 - 2 g y " " = - 19.6 y " " m^(2) s^(-2)`
These equations give the velocity and the distance travelled as a function of time and also the variation of velocity with distance. The variation of acceleration, velocity, and distance, with time have been plotted in Fig. 3.14 (a). (b) and (c)
(a)
(b)
(c)