$A$ body starts from the origin and moves along the $X$-axis such that the velocity at any instant is given by $v = (4t^3 - 2t)$,where $t$ is in $s$ and velocity is in $m/s$. What is the acceleration of the particle when it is $2\, m$ from the origin? (in $m/s^2$)

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

If the velocity of a body related to displacement $x$ is given by $v = \sqrt{5000 + 24x} \; \text{m/s}$,then the acceleration of the body is $\dots \dots \; \text{m/s}^2$.

If the velocity of a particle is given by $v = (180 - 16x)^{1/2} \text{ m/s}$,then its acceleration will be ....... $\text{m/s}^2$.

The velocity of a car travelling on a straight road is $3.6 \ km/h$ at an instant of time. Now,travelling with uniform acceleration for $10 \ s$,the velocity becomes exactly double. If the wheel radius of the car is $25 \ cm$,then which of the following is the closest to the number of revolutions that the wheel makes during this $10 \ s$?

$A$ particle starts moving with acceleration $2 \, m/s^2$. The distance travelled by it in the $5^{\text{th}}$ half-second is ....... $m$. (in $.25$)