The displacement $x$ (in $m$) of a particle of mass $m$ (in $kg$) moving in one dimension under the action of a force,is related to time $t$ (in $s$) by $t = \sqrt{x} + 3$. The displacement of the particle when its velocity is zero,will be

$A$ particle starting from rest moves with a uniform acceleration and covers $x$ meters in the first $5 \ s$. The same particle will cover the following distance in the next $5 \ s$:

$A$ particle starts with an initial speed $u$ and retardation $a$ to come to rest in time $T$. The time taken to cover the first half of the total path travelled is .......

The displacement of a particle after time $t$ is given by $x = (k/b^2)(1 - e^{-bt})$ where $b$ is a constant. What is the acceleration of the particle?

$A$ body starts with an initial velocity of $10\,m/s$ and moves along a straight line with constant acceleration. When the velocity of the particle is $50\,m/s$,the acceleration is reversed in direction. The velocity of the particle when it again reaches the starting point is $............\,m/s$.

$A$ particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, m/s$ to $20 \, m/s$ while passing through a distance of $135 \, m$ in $t$ seconds. The value of $t$ is..........$s$.