Question

Look at the graphs (A) to (D) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle
(a)

(b)


(c)
(d)

Answer 1

(a) Recall 1-D motion/motion in a straight -line.
If we draw a line-parallel to the vertical -axis,it intersects the graph at two points.That is the paticle has two positions at same instances. A particle cannot have two positions at the same instant of time.
Therefore,the given x-t graphs,shown in (a),does not represent one-dimensional motion of a particle.

(b) Recall 1-D motion/motion in a straight -line.
If we draw a line-parallel to the vertical -axis,it intersects the graph at two points.That is the paticle has two velocities at the same instance. A particle cannot have two velocities at the same instant of time.
Therefore,the given v-t graphs,shown in (b),does not represent one-dimensional motion of a particle.

(c) Speed particle is always positive.
The graph shows that the speed of the particle is negative at some – points. Speed of particle being a scalar quantity cannot be negative.
Therefore, the graph in (c), does not represent one dimensional motion of a particle

(d) Path length (distance) travelled by the particle is always positive
$\text{Distance}\ge |\text{Displacement}|$
in the figure (d). The total path length travelled by the particles is decreasing after sometime whereas the total path length travelled by the particle cannot decrease with time.
Therefore,the graph in (d),does not represent one dimensional motion.