The acceleration of a particle is increasing linearly with time $t$ as $a = 6t$. The particle starts from the origin with an initial velocity $u = 10 \ m/s$. The distance travelled by the particle after $t = 2 \ s$ will be: (in $m$)

If average and instantaneous velocities are same,then what is the type of motion?

$A$ rifle bullet loses $1/20^{th}$ of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is :-

$A$ lift of mass $M = 500 \, kg$ is descending with a speed of $2 \, ms^{-1}$. Its supporting cable begins to slip,thus allowing it to fall with a constant acceleration of $2 \, ms^{-2}$. The kinetic energy of the lift at the end of a fall through a distance of $6 \, m$ will be $........... \, kJ$.

The maximum possible acceleration of a train moving on a straight track is $10 \ m/s^2$ and maximum possible retardation is $5 \ m/s^2$. If the maximum achievable speed of the train is $10 \ m/s$,then the minimum time in which the train can complete a journey of $135 \ m$ starting from rest and ending at rest is ......... $s$.

$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = (t^3 - 6t^2 + 3t + 4) \ m$. Find the velocity of the particle in $m/s$ when its acceleration is zero.