$A$ force separately produces accelerations of $18 \ m/s^2$, $9 \ m/s^2$, and $6 \ m/s^2$ in three bodies of masses $P$, $Q$, and $R$ respectively. If the same force is applied on a body of mass $P+Q+R$, then the acceleration of that body is: (in $m/s^2$)

$A$ body of mass $500\,g$ moves along the $x$-axis such that its velocity varies with displacement $x$ according to the relation $v = 10\sqrt{x}\,m/s$. The force acting on the body is $...........\,N$.

The motion of a particle of mass $m$ is described by $y = ut + \frac{1}{2}gt^2$. Find the force acting on the particle.

$A$ particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$. Its kinetic energy after an interval $t$ is

The magnitude and direction of the acceleration produced in a body of mass $5 \text{ kg}$ when two mutually perpendicular forces $8 \text{ N}$ and $6 \text{ N}$ act on it, are respectively:

$A$ particle of mass $2/3 \, kg$ with velocity $v = -15 \, m/s$ at $t = -2 \, s$ is acted upon by a force $F = k - \beta t^2$. Here,$k = 8 \, N$ and $\beta = 2 \, N/s^2$. The motion is one-dimensional. Then,the speed at which the particle acceleration is zero again,is ........... $m/s$.