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________ $\mathrm{m} / \mathrm{s}.$

The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be

The graph below shows the velocity versus time graph for a body.

Which of the following graphs represents the corresponding acceleration $v/s$ time graph ?

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

The acceleration-time graph of a body is shown below The most probable velocity-time graph of the body is

The relation between time and distance is $t = \alpha {x^2} + \beta x$, where $\alpha $ and $\beta $ are constants. The retardation is