A swimmer can swim at a speed of $v$ in still water. He wants to cross a river flowing with speed $u$. If the width of the river is $d$ and the swimmer crosses the river in minimum time, what is the drift experienced by the swimmer?

Three particles start from the origin at the same time, one with a velocity ${v_1}$ along x-axis, the second along the y-axis with a velocity ${v_2}$ and the third along x=y line. The velocity of the third so that the three may always lie on the same line is

Two trains, each of length 100 m, are running on parallel tracks in opposite directions with speeds of 60 km/h and 40 km/h respectively. In what time will they completely cross each other?

A man is walking on a road with velocity $3$ km/h. Rain appears to fall vertically downwards to him. He increases his speed to $6$ km/h and finds that now the rain is falling at an angle of $45^\circ$ with the vertical. What is the speed of rain with respect to ground?

A 150m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot cross to train would be

A bird files for 4s with a velocity of $\left| {t - 2} \right|{\rm{m}}{{\rm{s}}^{ - 1}}$ in a straight line, where t=time in second. It covers a distance of

A car is moving east at 20 m/s and a cyclist is moving west at 10 m/s. What is the velocity of the car relative to the cyclist?

A bus is moving on a straight road with speed of 20 m/s. A man is driving a car behind bus in same direction. The driver of car observes bus to be moving at a speed of 10 m/s. The speed of car may be

A person walks on a moving escalator at 2 m/s in the direction of the escalator's motion. The escalator moves at 3 m/s. What is the person's velocity relative to the ground?

Which of the following are true?

(i) A body having constant speed can have verying velocity.

(ii) Position-time graphs for two objects with zero relative velocity are parallel.

(iii) The numerical ration of velocity to speed of an object can never be more than one.

The distance-time graphs of a particle at time t makes angle ${45^0}$ with the time axis. After two seconds, it makes an angle ${60^0}$ with the time axis. What is the average acceleration of the particle?