A particle moves along a straight line. Its position at any instant is given by $x=32 t-\frac{8 t^3}{3}$, where $x$ is in metre and $t$ is in second. Find the acceleration of the particle at the instant when particle is at rest $..........\,m / s ^2$

The potition $x$ of particle veries with time $t$ as $x = ct^2 + b,$ where $c, b$ are positive constant. Which of the following graph $s$ is correct

A particle is moving with speed $v= b\sqrt x$ along positive $x-$ axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at origin at $t = 0$ ).

Given below are two statements:
Statement $I:$ Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement $II:$ Area under acceleration- time graph is equal to the change in velocity- in the given time.
In the light of given statements, choose the correct answer from the options given below.