The relation between position $( x )$ and time ( $t$ ) are given below for a particle moving along a straight line. Which of the following equation represents uniformly accelerated motion? [where $\alpha$ and $\beta$ are positive constants]

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 velocity of a bullet is reduced from $200\,m/s$ to $100\,m/s $ while travelling through a wooden block of thickness $10\,cm$. The retardation, assuming it to be uniform, will be 

A particle of unit mass undergoes one­ dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ - 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20\,ms ^{-1}$ to a value approaching zero at $s=30\,m$, then acceleration of the particle at $s=15\,m$ is $........$

A particle initially at rest starts moving from reference point. $\mathrm{x}=0$ along $\mathrm{x}$-axis, with velocity $v$ that varies as $v=4 \sqrt{\mathrm{x} m} / \mathrm{s}$. The acceleration of the particle is __________$ \mathrm{ms}^{-2}$.