$A$ particle moves in a straight line and its position $x$ at time $t$ is given by $x^2 = 2 + t$. Its acceleration is given by

The speed of a body moving with uniform acceleration is $u$. This speed is doubled while covering a distance $S$. When it covers an additional distance $S$,its speed would become

$A$ rifle bullet loses $\left(\frac{1}{25}\right)^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet 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 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 $x=0$.

$A$ car moving with uniform acceleration covers a distance of $200 \,m$ in the first $2 \,s$ and a distance of $220 \,m$ in the next $4 \,s$. The velocity of the car after $7 \,s$ is: (in $\,m/s$)

$A$ car accelerates from rest at a constant rate $\alpha$ for some time,after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is $t$,then the maximum velocity acquired by the car is