Two trains travelling on the same track are approaching each other with equal speeds of $40\ m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\ km$ apart. Assuming the decelerations to be uniform and equal,the value of the deceleration to barely avoid collision should be..........$m/s^2$.

Object $A$ starts from rest with a constant acceleration $a$. Object $B$ starts from the same position and moves in the same direction as $A$ with a constant velocity $v$. If both meet after time $t$,then $t =$

If $x \propto t^{5/2}$,then

$A$ body starts from rest and moves with uniform acceleration. If the distance travelled by it in the first $2 \,s$ is $x_1$ and in the next $2 \,s$ is $x_2$, then $x_1$ and $x_2$ are related as

$A$ point moves such that its displacement as a function of time is given by $x^3 = t^3 + 1$. Its acceleration as a function of time $t$ will be

$m$ 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 $x = 0$.