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 velocity-displacement $(v-s)$ graph shows the motion of a particle moving in a straight line. The velocity-displacement graph is a circle of radius $2 \ m$ and the center is at $(2, 0) \ m$. The value of acceleration for this particle at a point $(2-\sqrt{2}, \sqrt{2}) \ m$ will be $ms^{-2}$.

$A$ woman starts from her home at $9.00\; am$, walks with a speed of $5\; km\; h^{-1}$ on a straight road up to her office $2.5\; km$ away, stays at the office up to $5.00\; pm$, and returns home by an auto with a speed of $25\; km\; h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

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 ........ $m$.

Draw the $x-t$ graphs which represent positive,negative,and zero velocity.

$A$ car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ seconds,the total distance travelled is