The velocity $(v)$-time $(t)$ graph for a particle moving along the $x$-axis is shown in the figure. The corresponding position $(x)$-time $(t)$ graph is best represented by:

Draw the $x-t$ graphs which represent positive,negative,and zero velocity.

The position $x$ of a particle at any time $t$ is given by $x(t) = 4t^3 - 3t^2 + 2$. The acceleration and velocity of the particle at $t = 2 \, s$ are respectively:

The velocity-time graph of a body moving along a straight line is shown in the figure. The ratio of the average velocities during the time intervals $t_1$ and $t_2$ 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 ........... $m/s^2$.

The $v-t$ graph of a rectilinear motion is shown in the adjoining figure. The distance from the starting point after $8 \text{ s}$ is .......... $\text{m}$.