Question

If the time-displacement graph of a particle is parallel to the time-axis, then velocity of the particle is:
A. infinity
B. unity
C. equal to acceleration
D. zero

Answer 1

The velocity is given by the time rate of change of the displacement. So in a time versus displacement graph the slope of the curve will represent the velocity. The slope of a curve is given by the $\tan$ of the angle which the curve makes with the x-axis.

Formulas used: $\text{slope=tan}\theta =\dfrac{\Delta y}{\Delta x}$

Complete answer:
Given that the time-displacement graph of a particle is parallel to the time-axis. That means if the distance-time graph of the object is parallel to the time axis then the particle has not covered any displacement with change in time. i.e. the particle is at rest. So the change of displacement of the particle with respect to time is zero so the velocity of the particle will be zero.
Usually time is taken in the x-axis and the displacement of the particle is taken in the y-axis. So if the graph is parallel to the time axis then the velocity of the particle is given by
$v=\dfrac{\Delta s}{\Delta t}=\dfrac{0}{\Delta t}=0$

So the correct option is D.

Additional Information:
The magnitude of displacement of a particle is defined as the length of the straight line joining the initial position of the particle to the final position of the particle. And the direction of displacement is from the initial position to the final position.

Note:
For a particle moving with constant velocity the displacement versus time graph will be a straight line making an angle $45{}^\circ$ with the time axis. Displacement versus time curve represents the position of the particle at different instant of time.