Three forces $F_1=10\,N$,$F_2=8\,N$,and $F_3=6\,N$ are acting on a particle of mass $5\,kg$. The forces $F_2$ and $F_3$ are applied perpendicular to each other such that the particle remains at rest. If the force $F_1$ is removed,then the acceleration of the particle is $......\,m/s^2$.

Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.

Which one of the following statements is incorrect?

$A$ block is placed on a rough horizontal plane. $A$ time-dependent horizontal force $F = kt$ acts on the block,where $k$ is a positive constant. The acceleration-time graph of the block is

Given $m_1 = 4m_2$. How much extra distance (in $cm$) does $m_2$ travel before coming to rest?

In the given figure, the blocks $A$, $B$, and $C$ weigh $4 \ kg$, $6 \ kg$, and $8 \ kg$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is . . . . . . $N$. (Use $g = 10 \ m/s^2$)