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 $m$)

$A$ particle moving with uniform acceleration travels $24\, m$ and $64\, m$ in the first two consecutive intervals of $4\, s$ each. Its initial velocity is ....... $m/s$.

The displacement of a particle starting from rest at $t=0$ is given by $s=9 t^2-2 t^3$. The time in seconds at which the particle will attain zero velocity is (in $s$)

$A$ body starts with an initial velocity of $10\,m/s$ and moves along a straight line with constant acceleration. When the velocity of the particle is $50\,m/s$,the acceleration is reversed in direction. The velocity of the particle when it again reaches the starting point is $............\,m/s$.

$A$ bullet enters a wooden block with velocity $120 \,m/s$. The bullet travels $1.5 \,s$ in the block before its velocity reduces to zero due to a resistance force which is proportional to the square root of the velocity. The distance travelled by the bullet in the wooden block is (in $\,m$)

Velocity of a body moving along a straight line with uniform acceleration $a$ reduces by $\frac{3}{4}$ of its initial velocity in time $t_0$. The total time of motion of the body till its velocity becomes zero is