Relative Velocity

Explain the concept of the relative velocity. Draw position-time graphs of two objects moving along a straight line when their relative velocity is (i) zero and (ii) non-zero.

Derive the second and third equations of motion by calculus method.

A car moving on a straight line covers a distance at speed $\mathrm{v}$ and the return journey with a speed of $2\mathrm{v}$ Find (i) average speed and (ii) mean speed.

Two trains$\mathrm{A} \mathrm{and} \mathrm{B}$ of length $350\mathrm{m}$ each are moving on two parallel tracks with equal velocities of $100 \mathrm{km}/\mathrm{hr}$ in the same direction, $A$

ahead of $B$. The driver of $B$desires to overtake $\mathrm{A}$.and accelerates by $1 {\mathrm{ms}}^{-2.}$. If after $50 \sec .$ The guard of $B$ just brushes past the driver of $A$, then the original distance between the guard of $\text{B}$ and the driver of $\mathrm{A}$ is :

A man in a lift ascending with an acceleration throws a ball vertically up with a velocity $V$ and catches it after time $3 \sec$. Afterwards when the lift is descending with the same acceleration, the man again throws the ball vertically up with the same velocity and catches it after $1 \sec$. Find $V$ (use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

A lift in which a man is standing, is moving upward with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ The man drops a coin from a height of $4.9 \mathrm{m}$ and if $g=9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, then the coin reaches the floor of the lift after a time of $1 \mathrm{s}$.

The magnitude of velocity of a man with respect to ground is 

A boat moves with a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ relative to water in a river flowing with a speed of $3 \mathrm{km} {\mathrm{h}}^{-1}$ and having a width of $1 \mathrm{km}.$ What will be the minimum time taken around a round trip ?

Two bodies with initial velocity $v_0$ are thrown simultaneously from a tower. One is thrown vertically upward and another is thrown vertically downward. After time $t$, the distance between the bodies will be 

A bus is moving on a straight road with a speed of $10 \mathrm{m} {\mathrm{s}}^{–1}$ while a scooterist wishes to overtake the bus in $100 \mathrm{s}$. If the bus is at a distance of $100 \mathrm{m}$ from the scooterist with what speed should the scooterist chase the bus?

A body can be at rest and in motion at the same time.

Rest is a relative term.

To find the speed of a river's current, a boatman decides to carry out the following experiment. He drops a wooden bar into the water and he sets off downstream, rowing along the flow of river. After $40 \min$, he reaches point $A$, $1 \mathrm{km}$ from his starting point, and turns back. After travelling some distance upstream, he picks up the bar then quickly turns around again and, rowing downstream once more, reaches $A$ for the second time $24 \min$ after picking the bar. Assuming that the speeds of both current and the boat relative to water are constant, what is the speed of the current?

A jet airplane travelling at the speed of $500\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ ejects its products of combustion at the speed of $1500\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ relative to the jet plane. The speed of the products of combustion with respect to an observer on the ground is

On a two-lane road, car A is travelling with a speed of $36\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}.$ Two cars B and C approach car A in opposite directions with a speed of $54\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$each. At a certain instant, when the distance AB is equal to AC, both being $1 \mathrm{km}$, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident is

What is the relative velocity of a car $A$ with respect to car $B$, if car $A$ is moving with $60 \mathrm{km} {\mathrm{h}}^{-1}$ towards east and car $B$ is moving with $45 \mathrm{km} {\mathrm{h}}^{-1}$ towards west?

A person in an elevator accelerating upwards with an acceleration of $2\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, toss a coin vertically upwards with a speed of $20\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. After how much time will the coin fall back into his hand? ( take$\mathrm{g}=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$)

An aircraft is flying at a height of $3400 \mathrm{m}$ above the ground. If the angle subtended at a ground observation point by the aircraft position $10\mathrm{ }\mathrm{s}$ apart is $30°$, then the speed of the aircraft is