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 .......... $\text{m}$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance (in $m$) traversed by the particle between $t=0\; s$ and $t=10\; s$.

The velocity $(v)$ of a particle moving along the $x$-axis varies with its position $(x)$ as shown in the figure. How does the acceleration $(a)$ of the particle vary with position $(x)$?

From the $v-t$ graph,find the total distance covered by the car in time $t = t_1 + t_2$.

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_1$ to $t_2$?
$(a)$ $x(t_2) = x(t_1) + v(t_1)(t_2 - t_1) + (1/2)a(t_2 - t_1)^2$
$(b)$ $v(t_2) = v(t_1) + a(t_2 - t_1)$
$(c)$ $v_{\text{average}} = (x(t_2) - x(t_1)) / (t_2 - t_1)$
$(d)$ $a_{\text{average}} = (v(t_2) - v(t_1)) / (t_2 - t_1)$
$(e)$ $x(t_2) = x(t_1) + v_{\text{average}}(t_2 - t_1) + (1/2)a_{\text{average}}(t_2 - t_1)^2$
$(f)$ $x(t_2) - x(t_1) = \text{area under the } v-t \text{ curve bounded by the } t\text{-axis and the dotted lines shown.}$

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure,for a time interval of $40 \text{ s}$. The total distance travelled by the particle and the average velocity during this period are,respectively . . . . . . .