Question
Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.
Solution
(a) From position-time graph we can find the position of the particle at any instant by drawing the perpendicular on time axis at that instant.
There are two different positions of particle at a particular instant which is not possible because position is a single valued function.
There are two different positions of particle at a particular instant which is not possible because position is a single valued function.
(b) Since velocity is a single valued function, therefore at any instant, the particle cannot have two different velocities, hence the graph cannot represent motion.
(c) Since speed is magnitude of velocity which cannot be negative, therefore, graph is not possible.
(d) Total length of path travelled by particle cannot decrease with the time. Therefore, graph is not possible.
