The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in $4 \; s$ is ......... $m$.

The diagram shows the variation of $1/v$ (where $v$ is the velocity of the particle) with respect to time $t$. Using the details given in the graph,the instantaneous acceleration at time $t = 3\,s$ will be equal to $...........\,m/s^2$.

What does $\dot x$ represent?

The speed-time graph of a particle moving along a fixed direction is shown in the figure. The distance traversed by the particle between $t = 2\,s$ to $t = 6\,s$ is........$m$

The figure shows a velocity-time graph of a particle moving along a straight line. If the particle starts from the position $x_0 = -15 \, m$,then its position at $t = 2 \, s$ will be ........ $m$.

The velocity of a particle moving on the $x$-axis is given by $v = x^2 + x$,where $v$ is in $m/s$ and $x$ is in $m$. Find its acceleration in $m/s^2$ when passing through the point $x = 2 \ m$.