The displacement is given by $x = 2{t^2} + t + 5$, the acceleration at $t = 2\;s$ is.........$m/{s^2}$

Particle $A$ is moving along $x$-axis. At time $t=0$, it has velocity of $10\,m / s$ and acceleration $-4\,m / s ^2$. Particle $B$ has velocity of $20\,m / s$ and acceleration $-2\,m / s ^2$. Initially, both the particles are at origin. At time $t=2\,s$, distance between the two particles is $.............\,m$

Explain the acceleration.

A particle is projected with velocity $v_{0}$ along $x-$ axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e., $ma =-\alpha x ^{2}.$ The distance at which the particle stops:

What is reaction time ? On what does the reaction time depend ?

The position$(x)$ of a particle at any time$(t)$ is given by $x(t) = 4t^3 -3t^2 + 2$ The acceleration and velocity of the particle at any time $t = 2\, sec$ are respectively