Two boats $A$ and $B$ are moving along perpendicular paths in a still lake at night. Boat $A$ move with a speed of $3{\mathrm{MS}}^{-1}$ and boat $B$ moves with a speed of $4{\mathrm{MS}}^{-1}$ in the direction such that they collide after sometime. At $t=0,$ the boats are $300\mathrm{m}$ apart. the ratio of distance travelled by boat $A$ to the distance travelled by boat $B$ at the instant of collision is:

A trolley is moving horizontally with a constant velocity of  $v m{s}^{-1}$ $\mathrm{w}.\mathrm{r}.\mathrm{t}.$ earth. $\mathrm{A}$ man starts running from one end of the trolley with a velocity of $1.5{\mathrm{vms}}^{-1}\mathrm{w}.\mathrm{r}.\mathrm{t}.$ to trolley. after reaching the opposite end, the man return back and continues running with a velocity $1.5{\mathrm{vms}}^{-1}\mathrm{w}.\mathrm{r}.\mathrm{t}.$ the trolley in the backward direction. If the length of the trolley is $L$ then the displacement of the man with  respect to earth during the process will be:

A particle $P$ is projected from a point on the surface of smooth inclined plane ( see figure). simultaneously another particle $Q$ is released on the smooth inclined plane from the same position.$P$and $Q$ collide after $t=4$ second. the speed of projection of $P$ is:

The figure shows the velocity time graph of a particle which moves along a straight line starting with velocity at $5 \mathrm{m} {\sec }^{-1}$ and coming to rest at $t=30\mathrm{s}$. Then :