A body of mass $2\, kg$ travels according to law $x = at + bt^2 + ct^3$, where $a = 3\, m/s$, $b = 4\,m/s^2$ and $c = 5\, m/s^3$, then force acting on body at $t = 2\, s$  ……… $N$.

In which of the following cases forces may not be required to keep the

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 ……….. $m/s$

A body of mass $2\, kg$ moves under a force of $(2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N$. It starts from rest and was at the origin initially. After $4 \,s$, its new coordinates are $(8, b, 20)$. The value of $b$ is …….. . (Round off to the Nearest Integer)

A vehicle of $100\, kg$ is moving with a velocity of $5 \,m/sec$. To stop it in $\frac{1}{{10}}\sec $, the required force in opposite direction is ……….. $N$