$A$ particle with initial velocity $v_0$ moves with constant acceleration $a$ in a straight line. Find the distance travelled in the $n^{th}$ second.

$m$ mass particle is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle,always pointing toward the equilibrium position $E$. The magnitude of $F$ is constant except at $E$ where it is zero. The particle is displaced a distance $A$ to the left of $E$ and released from rest at $t = 0$. Find the minimum time taken to reach from $x = -A/2$ to $x = 0$.

The $v^2$ versus $s$ graph of a particle moving in a straight line is shown in the figure. From the graph,some conclusions are drawn. State which statement is wrong?

$A$ particle moves along a straight line. Its position at any instant is given by $x = 32t - \frac{8t^3}{3}$,where $x$ is in $m$ and $t$ is in $s$. Find the acceleration of the particle at the instant when the particle is at rest $..........\,m/s^2$.

$A$ body travels $102.5 \ m$ in the $n^{\text{th}}$ second and $115.0 \ m$ in the $(n+2)^{\text{th}}$ second. The acceleration is: (in $m/s^2$)

$A$ particle is projected with velocity $v_0$ along the $x$-axis. The deceleration of the particle is proportional to the square of the distance from the origin,i.e.,$a = -\alpha x^2$. The distance at which the particle stops is: