The velocity-time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time $0$ to $10\,s$ is

Among the four graphs shown in the figure,there is only one graph for which the average velocity over the time interval $(0, T)$ can vanish for a suitably chosen $T$. Which one is it?

If the position-time graph of a particle is a sine curve as shown,what will be its velocity-time graph?

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:

Two trains, which are moving along different tracks in opposite directions, are put on the same track by mistake. On noticing the mistake, when the trains are $300 \, m$ apart, the drivers start slowing down the trains. The graphs given below show the decrease in their velocities as a function of time. The separation between the trains when both have stopped is: (in $ \, m$)

The relation between velocity $v$ and displacement $x$ is $v = x^2$. Find the acceleration at $x = 3 \ m$.