For a body moving with uniform acceleration along a straight line, the variation of its velocity $(v)$ with position $(x)$ is best represented by:

$A$ bullet from a gun is fired into a rectangular wooden block with velocity $u$. When the bullet travels $24\,cm$ through the block along its length horizontally,the velocity of the bullet becomes $\frac{u}{3}$. It then further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is $........\,cm$.

Two cars leave one after the other and travel with an acceleration of $0.4\, m/s^2$. Two minutes after the departure of the first,the distance between the cars becomes $1.9\, km$. The time interval between the departures of the cars is ........$s$.

If a body having initial velocity zero is moving with uniform acceleration $8\,m/s^2$,the distance travelled by it in the fifth second will be.........$m$.

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 velocity of a particle is $v = v_{0} + gt + Ft^{2}$. Its position is $x = 0$ at $t = 0$; then its displacement after time $t = 1$ is: