Motion in a Straight Line

The displacement of a particle moving along a straight line is related to time as $\sqrt{x}=t-3$. The displacement of the particle when its velocity is zero is

The driver of a bus moving at an speed of $60 \mathrm{km} {\mathrm{hr}}^{-1}$ saw a man at a distance of $52 \mathrm{m}$ from the bus. The driver stopped the car at a distance of $2 \mathrm{m}$ from the man using brake. The time required to stop the bus is

A ball of mass $m$ is thrown upward with a velocity $v$. The air exerts an average resisting force $F$. The velocity with which the ball returns to the thrower is

The equation of motion of a body is, $\frac{\mathrm{d}v\left(t\right)}{\mathrm{d}t}=9-3v\left(t\right)$ where, $v\left(t\right)$ is the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) at time $t$ (in second). If the body was at rest at $t=0$, then which of the following is correct?

Two uniformly dense spherical balls of radius $R$ and $2R$ are released simultaneously from identical heights. If both the balls hit the ground at the same time, then the ratio of densities of the balls, ${\rho }_{\mathrm{R}}:{\rho }_{2\mathrm{R}}$ is (here, ${\rho }_{\mathrm{R}}$is the density of the ball with radius $R$ and ${\rho }_{2\mathrm{R}}$ is the density of the ball with radius $2R$)

Water-drops are falling at regular intervals from a water tap situated at a height of $5 \mathrm{meters}$ from the ground. Just at the moment, the first drop touches the ground, the third drop comes out. At that moment, the height of the second drop of water from the ground will be