The distance travelled by an object in time $t$ is given by $s = 2.5 t^2$. The instantaneous speed of the object at $t = 5\,s$ will be $....\,m/s$.

Fill in the blanks:
$(a)$ The path length is always ............ .
$(b)$ The slope of the velocity-time graph for an object moving with acceleration is ............ .
$(c)$ If the velocity-time graph is parallel to the time-axis,the object is ............ .

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

$A$ particle of mass $50 \, g$ moves on a straight line. The variation of speed with time is shown in the figure. Find the force acting on the particle at $t = 2, 4,$ and $6 \, s$.

The $x-t$ graph for a uniformly accelerated particle is as shown in the figure. Find the average velocity between points $(i)$ and $(ii)$ in $ms^{-1}$.

The distance covered by the particle in the last $2\,s$ is what fraction of the total distance covered by it in $7\,s$?