K K Sharma Solutions for Chapter: Motion in a Straight Line, Exercise 1: TOPICWISE QUESTIONS

The acceleration of a particle, starting from rest, varies with the time according to the relation $a=-S{\omega }^2 \cos \left(\omega t\right)$. The displacement of this particle at time $t$ will be

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

The distance between two particles is decreasing at a rate of $6 \mathrm{m} {\mathrm{s}}^{-1}$. If these particles travel with 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

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

A person walks up a stalled escalator in $90 \mathrm{s}$. When standing on the same escalator, which is now moving, he is carried in $60 \mathrm{s}$. The time he would take to walk up the moving escalator will be

Two trains, each of length $50 \mathrm{m}$, are running with constant speeds, on parallel tracks. While moving in same direction, one overtakes the other in $40 \mathrm{s}$ and while moving in opposite directions, one crosses the other in $20 \mathrm{s}$. The speed of trains will be

Three elephants, $A$, $B$ and $C$, are moving along a straight line with constant speed, in the same direction, as shown in the figure. Speed of $A$ is $5 \mathrm{m} {\mathrm{s}}^{-1}$ and speed of $C$ is $10 \mathrm{m} {\mathrm{s}}^{-1}$. Initially, the separation between $A$ and $B$ is $d$ and between $B$ and $C$ is also $d$. When $B$ catches $C$, the separation between $A$ and $C$ becomes $3d$. Then, the speed of $B$ will be

A jet aeroplane traveling from east to west, at a speed of $500 \mathrm{km} {\mathrm{h}}^{-1}$, ejects out gases of combustion at a speed of $1500 \mathrm{km} {\mathrm{h}}^{-1}$, with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?