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 $v-t$ graphs of two moving objects make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. Find the ratio of their accelerations.

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha, \text{and } \beta$ are positive constants. The velocity of the particle will:

Figures $(i)$ and $(ii)$ below show the displacement-time graphs of two particles moving along the x-axis. We can say that

$A$ scooter accelerates from rest for time $t_{1}$ at a constant rate $a_{1}$ and then retards at a constant rate $a_{2}$ for time $t_{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be ..... .

The displacement-time graph for two particles $A$ and $B$ are straight lines inclined at angles of $30^\circ$ and $60^\circ$ with the time axis. The ratio of velocities $V_A:V_B$ is