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 $x-t$ graph of a particle moving along a straight line is shown in the figure. The $a-t$ graph of the particle is correctly shown by:

The velocity-time $(v-t)$ graph for a moving object is shown in the figure. The total displacement of the object during the time interval when there is non-zero acceleration and retardation is ........ $m$.

Match Column-$I$ with Column-$II$:

$A$ 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:

We have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?