$A$ particle located at $x= 0$ at time $t= 0$ starts moving along the positive $x-$direction with a velocity $v$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle varies with time as:

$A$ body is moving with uniform acceleration,describing $40 \, m$ in the first $5 \, s$ and $65 \, m$ in the next $5 \, s$. Its initial velocity will be . . . . . . $m/s$.

Brakes are applied in a car moving with a speed of $20\ m/s$,which produces a retardation of $5\ m/s^2$. The distance travelled by the car until it stops is ........ $m$.

$A$ particle is projected with velocity $v_0$ along the $x$-axis. The deceleration of the particle is proportional to the square of the distance from the origin,i.e.,$a = -\alpha x^2$. The distance at which the particle stops is:

$A$ car moving with a speed of $40 \, km/h$ can be stopped by applying brakes after at least $2 \, m$. If the same car is moving with a speed of $80 \, km/h$,what is the minimum stopping distance in meters?

$A$ goods train accelerating uniformly on a straight railway track approaches an electric pole standing on the side of the track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity of: