Which of the following graphs are straight lines ?
A. Distance – time graph of a body at rest
B. Velocity – time graph of a body moving with uniform acceleration
C. Distance – time graph of a body moving with uniform acceleration
D. Velocity – time graph of a body at rest
Choose the correct option :

The correct option is A, B and D.

Let us analyze each statement step-by-step:

Statement A: Distance – time graph of a body at rest
When a body is at rest, its distance (or position) relative to a reference point does not change over time. Therefore, the distance-time graph is a horizontal straight line parallel to the time axis.

Statement B: Velocity – time graph of a body moving with uniform acceleration
Acceleration is defined as the rate of change of velocity with respect to time ($a=\frac{dv}{dt}$). If acceleration $a$ is uniform (constant), velocity increases linearly with time ($v=u+at$). Hence, the velocity-time graph is an inclined straight line with a constant slope equal to the acceleration.

Statement C: Distance – time graph of a body moving with uniform acceleration
For a body moving with uniform acceleration $a$, the distance traveled $s$ in time $t$ is given by the kinematic equation:

$s=ut+\frac{1}{2}a{t}^2$

Statement D: Velocity – time graph of a body at rest
When a body is at rest, its velocity is zero for all time intervals. Therefore, the velocity-time graph is a straight line coinciding with the time axis (or parallel to it at $v=0$).

Thus, statements A, B, and D represent straight-line graphs.