Give examples of a one-dimensional motion where
a) the particle moving along positive x-direction comes to rest periodically and moves forward
b) the particle moving along positive x-direction comes to rest periodically and moves backward
(a) Let us consider a motion where
Thus,
&
(ii) Let us consider a function of motion where,
Thus the displacement of the particle is in negative direction and it comes to rest periodically.
Thus,
is a periodic function.
Now,
After zero displacement, velocity changes periodically.
Thus, is the function required.
(i) Now, let us consider a function
Thus, the particle moves in a positive direction, periodically with zero displacements.
Hence is the required function.