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

The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?

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

Which of the following graphs represents uniform motion?

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

$A$ particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$,where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by: