The distance travelled by a particle is proportional to the squares of time, then the particle travels with
The velocity $v$ of a particle moving along $x$-axis varies with its position $(x)$ as $v=\alpha \sqrt{x}$; where $\alpha$ is a constant. Which of the following graph represents the variation of its acceleration (a) with time $(t)$ ?
A truck starts from rest and accelerates uniformly at $2.0\; m s ^{-2} .$ At $t=10\; s$, a stone is dropped by a person standing on the top of the truck ($6 \;m $ high from the ground). What are the $(a)$ velocity, and $(b)$ acceleration of the stone at $t= 11\;s$? (Neglect atr resistance.)
For a train engine moving with speed of $20 \;ms ^{-1}$. the driver must apply brakes at a distance of $500 \;m$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{ x }\; ms ^{-1}$. The value of $x$ is $..............$ (Assuming same retardation is produced by brakes)