A small block slides down on a smooth inclined plane, starting from rest at time $t=0 .$ Let $S_{n}$ be the distance travelled by the block in the interval $\mathrm{t}=\mathrm{n}-1$ to $\mathrm{t}=\mathrm{n} .$ Then, the ratio $\frac{\mathrm{S}_{\mathrm{n}}}{\mathrm{S}_{\mathrm{n}+1}}$ is
$\frac{2 n-1}{2 n}$
$\frac{2 n-1}{2 n+1}$
$\frac{2 n+1}{2 n-1}$
$\frac{2 n}{2 n-1}$
A particle moving with a uniform acceleration travels $24\, m$ and $64\, m$ in the first two consecutive intervals of $4\, sec$ each. Its initial velocity is......$m / \sec $
A train moves from rest with a uniform acceleration $a$ . Attaining a maximum speed $v$ it starts moving with uniform retardation $a$ . Assuming $s$ = total distance covered in the unidirectional motion of the train, its total time of journey and maximum speed are (respectively).
An alpha particle enters a hollow tube of $4 \,m$ length with an initial speed of $1 \,km/s$. It is accelerated in the tube and comes out of it with a speed of $9 km/s$. The time for which it remains inside the tube is
An object at rest at the origin begins to move in the $+x$-direction with a uniform acceleration of $1 \,m / s ^2$ for $4 \,s$ and then it continues moving with a uniform velocity of $4 \,m / s$ in the same direction.The $x-t$ graph for object's motion will be