The position of a particle moving along the $x$-axis is given by $x = (-2t^3 + 3t^2 + 5) \ m$. The acceleration of the particle at the instant its velocity becomes zero is ....... $m/s^2$.

If the velocity of a particle is $v = At + Bt^2$,where $A$ and $B$ are constants,then the distance travelled by it between $1 \ s$ and $2 \ s$ is

$A$ particle of mass $m$ is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example,when the particle is to the left of $E$,$F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards the left from the equilibrium position $E$ and released from rest at $t = 0$. What is the period of the motion?

The position of a particle as a function of time $t$ is given by $x(t) = at + bt^2 - ct^3$,where $a, b,$ and $c$ are constants. When the particle attains zero acceleration,its velocity will be:

$A$ body $A$ starts from rest with an acceleration $a_1$. After $2$ seconds,another body $B$ starts from rest with an acceleration $a_2$. If they travel equal distances in the $5$th second after the start of $A$,then the ratio $a_1:a_2$ is equal to

$A$ bullet moving with a velocity of $200 \, cm/s$ penetrates a wooden block and comes to rest after traversing $4 \, cm$ inside it. What velocity is needed for travelling a distance of $9 \, cm$ in the same block? (in $cm/s$)