The $v - t$ graph of a moving object is given in figure. The maximum acceleration is...........$\mathrm{cm/sec}^{2}$

A particle is moving in one dimension (along $\mathrm{x}$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position ( $\mathrm{x}$ ) with time ( $\mathrm{t})$ is given as $\mathrm{x}=-3 \mathrm{t}^5+18 \mathrm{t}^2+16 \mathrm{t}$, where $\mathrm{x}$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$. The velocity of the particle when its acceleration becomes zero is________ $\mathrm{m} / \mathrm{s}.$

A particle moving along $x-$axis has acceleration $f$, at time $t$ , given by $ f=f_0$$\left( {1 - \frac{t}{T}} \right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity . In the time interval between $t=0$ and the instant when $f=0$ , the particle 's velocity $(v_x)$ is 

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

Refer to the graph in figure. Match the following

Graph	Characteristics
$(A)$	$(i)$ has $v > 0$ and $a < 0$ throughout
$(B)$	$(ii)$ has $x > 0,$ throughout and has a point with $v = 0$ and a point with $a = 0$
$(C)$	$(iii)$ has a point with zero displacement for $t > 0$
$(D)$	$(iv)$ has $v < 0$ and $a > 0$