From the $v-t$ graph,the

The accompanying graph of position $x$ versus time $t$ represents the motion of a particle. If $p$ and $q$ are both positive constants,the expression that best describes the acceleration $a$ of the particle is

The position $(x)$ of a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. The average acceleration of the particle in the time interval $t=0$ to $t=8 \, s$ is ........... $m/s^2$.

$A$ woman starts from her home at $9.00\; am$, walks with a speed of $5\; km\; h^{-1}$ on a straight road up to her office $2.5\; km$ away, stays at the office up to $5.00\; pm$, and returns home by an auto with a speed of $25\; km\; h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

Given below are two statements:
Statement $I:$ Area under velocity-time graph gives the displacement of the body in a given time.
Statement $II:$ Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given statements, choose the correct answer from the options given below.

The graph shows the variation with time $t$ of velocity $v$ of an object moving along a straight line. The $a-t$ graph will be: