$A$ body starts moving from rest with constant acceleration. It covers a displacement $S_1$ in the first $(p-1)$ seconds and $S_2$ in the first $p$ seconds. The total displacement $S_1+S_2$ will be covered in time:

$A$ 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 constant 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 $t=0$. Find the minimum time it will take to reach from $x=-A/2$ to $x=0$.

$A$ body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

$A$ small block slides down on a smooth inclined plane,starting from rest at time $t=0$. Let $S_{n}$ be the distance travelled by the block in the interval $t=n-1$ to $t=n$. Then,the ratio $\frac{S_{n}}{S_{n+1}}$ is

The velocity of a train increases uniformly from $20 \; km/h$ to $60 \; km/h$ in $4 \; hours$. The distance travelled by the train during this period is .......... $km$.

$A$ body is moving along a straight line with initial velocity $v_0$. Its acceleration $a$ is constant. After $t$ seconds,its velocity becomes $v$. The average velocity of the body over the given time interval is