BM Sharma Solutions for Chapter: Motion in One Dimension, Exercise 5: DPP

The distance between two particles is decreasing at the rate of $6 \mathrm{m} {\mathrm{s}}^{-1}.$ If these particles travel with the same speeds and in the same direction, then the separation increases at the rate of $4 \mathrm{m} {\mathrm{s}}^{-1}$. The particles have speeds as

A boat moves with a speed of $4 \mathrm{km} {\mathrm{h}}^{-1}$ relative to water in a river, flowing with a speed of $3 \mathrm{km} {\mathrm{h}}^{-1}$ and having a width of $1 \mathrm{km}$. The minimum time taken around a round trip is

An express train is moving with a velocity $v_1$. Its driver finds another train moving on the same track in the same direction with velocity $v_2$. To escape collision, the driver applies a retardation $a$ on the train. The minimum time of escaping the collision will be

A thief is running away on a straight road in a jeep moving at a speed of $9 \mathrm{m} {\mathrm{s}}^{-1}$. A policeman chases him on a motorcycle moving at the speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. If the initial separation of the jeep from the motorcycle is $100 \mathrm{m},$ how long will it take for the police to catch the thief?

Two trains, one of length $100 \mathrm{m}$ and another of length $125 \mathrm{m},$ moving in mutually opposite directions along parallel lines, meet each other, each with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$. If their accelerations are $0.3 \mathrm{m} {\mathrm{s}}^{-2}$ and $0.2 \mathrm{m} {\mathrm{s}}^{-2}$ respectively, then, the time they take to pass each other will be

Two cars are moving in the same direction with the same speed $30 \mathrm{km} {\mathrm{h}}^{-1}$. They are separated by a distance of $5 \mathrm{km}$. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of $4$ $\mathrm{minutes}$ will be

A boat takes $2 \mathrm{h}$ to travel $8 \mathrm{km}$ and back in still water. If the velocity of water is $4 \mathrm{km} {\mathrm{h}}^{-1}$, the time taken for going upstream $8 \mathrm{km}$ and coming back is

A man in a lift, ascending with an upward acceleration $a$, throws a ball vertically upwards with a velocity $v$, with respect to himself and catches it after $t_1\mathit{ }\mathrm{s}$. Afterwards when the lift is descending with the same acceleration $a$, acting downwards, the man again throws the ball vertically upwards with the same velocity with respect to him and catches it after $t_2 \mathrm{s}$. Which of the following statements is/are correct?