$A$ car accelerates from rest at a constant rate of $2 \ m/s^2$ for some time. Then it retards at a constant rate of $4 \ m/s^2$ and comes to rest. If it remains in motion for $3 \ s$,then the total displacement covered by it is $.... \ m$.

An alpha particle enters a hollow tube of $4 \, m$ length with an initial speed of $1 \, km/s$. It is accelerated in the tube and comes out of it with a speed of $9 \, km/s$. The time for which it remains inside the tube is

$A$ body of mass $4 \,kg$ is accelerated by a constant force. It travels a distance of $5 \,m$ in the first second and a distance of $2 \,m$ in the third second. The force acting on the body is: (in $\,N$)

$A$ particle moves for $8 \, s$. It first accelerates from rest and then retards to rest. If the retardation is $3 \, times$ the acceleration, then the time for which it accelerates is: (in $s$)

$A$ particle starts moving along a line from zero initial velocity and comes to rest after moving a distance $d$. During its motion,it has a constant acceleration $f$ over $2/3$ of the distance and covers the rest of the distance with constant retardation. The total time taken to cover the distance is

The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres,where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is