Question

A particle starts from origin $O$, from rest, and moves with a uniform acceleration, along the positive $x-$axis. Identify all figures that correctly represent the motion qualitatively ($a=$ acceleration, $v=$ velocity, $x=$displacement, $t=$ time)

• A. $\text{(A)}$
• B. $\text{(A), (B), (D)}$
• C. $\text{(A), (B), (C)}$
• D. $\text{(B), (C)}$

Answer 1

The correct option is B $\text{(A), (B), (D)}$

For constant acceleration, the $a-t$ graph is a straight line and parallel to the time axis.

The $v-t$ graph will be a straight line passing through origin $(\text{as}u=0)$ and the slope of the line will be equal to acceleration.

The $x-t$ graph will be a parabola, indicating that the displacement is positive and increases non-linearly with time.

The graphs depicted in diagrams (A), (B) and (D) are correctly representing the above points.

Hence, $\left(D\right)$ is the correct answer.