The position of a particle moving along the $y-$ axis is given as $y = 3t^2 - t^3$,where $y$ is in $m$ and $t$ is in $s$. The time when the particle attains the maximum positive position will be ........ $s$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. What is the average speed of the particle over the intervals: $(a)$ $t = 0\; s$ to $10\; s$,and $(b)$ $t = 2\; s$ to $6\; s$?

The displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

$A$ car starts from rest and travels with uniform acceleration $\alpha$ for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of the car is $t$,the maximum velocity attained by it is given by:

The figure shows the graph of the $x$-coordinate of a particle moving along the $x$-axis as a function of time. The average velocity during $t=0$ to $6 \,s$ and the instantaneous velocity at $t=3 \,s$ respectively,will be

$A$ 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