Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t = 0, the distance between them is 90 km, the time when they collide is

(a) 1 hr

(2) 2 hr

(3) 3 hr

(4) 4 hr

Concept Questions :-

Relative motion
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A steam boat goes across a lake and comes back (a) On a quite day when the water is still and (b) On a rough day when there is uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both days was same, in which case it will complete the journey in lesser time

(1) Case (a)

(2) Case (b)

(3) Same in both

(4) Nothing can be predicted

Concept Questions :-

Relative motion
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To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of $25\sqrt{3}$ km/hr. The actual velocity of the train will be

(1) 25 km/hr

(2) 50 km/hr

(3) 5 km/hr

(4) $5\sqrt{3}$ km/hr

Concept Questions :-

Relative motion
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A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus

(1) 50 m/s

(2) 40 m/s

(3) 30 m/s

(4) 20 m/s

Concept Questions :-

Relative motion
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Two particles having position vectors $\stackrel{\to }{{r}_{1}}=\left(3\stackrel{^}{i}+5\stackrel{^}{j}\right)$ metres and $\stackrel{\to }{{r}_{2}}=\left(-5\stackrel{^}{i}-3\stackrel{^}{j}\right)$ metres are moving with velocities ${\stackrel{\to }{v}}_{1}=\left(4\stackrel{^}{i}+3\stackrel{^}{j}\right)\text{\hspace{0.17em}}m/s$ and ${\stackrel{\to }{v}}_{2}=\left(\alpha \text{\hspace{0.17em}}\stackrel{^}{i}+7\stackrel{^}{j}\right)$ m/s. If they collide after 2 seconds, the value of ‘α’ is-

(1) 2

(2) 4

(3) 6

(4) 8

Concept Questions :-

Speed and velocity
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A vector $\stackrel{\to }{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $|\Delta \stackrel{\to }{a}|$ and $\Delta a$ are respectively

1. $0,\text{\hspace{0.17em}}a\text{\hspace{0.17em}}d\text{​}\theta$

2. $a\text{\hspace{0.17em}}d\text{​}\theta ,\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$

3. 0, 0

4. None of these

Concept Questions :-

Position and displacement
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A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h then the velocity of river water is

(1) 4 km/h

(2) 6 km/h

(3) 8 km/h

(4) 10 km/h

Concept Questions :-

Relative motion
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A 120 m long train is moving towards west with a speed of 10 m/s. A bird flying towards east with a speed of 5 m/s crosses the train. The time taken by the bird to cross the train will be

(1) 16 sec

(2) 12 sec

(3) 10 sec

(4) 8 sec

Concept Questions :-

Relative motion
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A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is

(1) 2h

(2) 2h 40 min

(3) 1h 20 min

(4) Cannot be estimated with the information given

Concept Questions :-

Relative motion
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A man sitting in a bus travelling in a direction from west to east with a speed of 40 km/h observes that the rain-drops are falling vertically down. To the another man standing on ground the rain will appear

(1) To fall vertically down

(2) To fall at an angle going from west to east

(3) To fall at an angle going from east to west

(4) The information given is insufficient to decide the direction of rain.

Concept Questions :-

Relative motion
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