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)
$100$
$101$
$520$
$200$
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 train starting from rest accelerates uniformly for $100\,\,s,$ then comes to a stop with a uniform retardation in the next $200\,\,s.$ During the motion, it covers a distance of $3\,\,km.$ Choose the wrong option
A body moves from rest with a constant acceleration of $5\,m/{s^2}$. Its instantaneous speed (in $m/s)$ at the end of $10\, sec$ is