A car is standing \(200~\text{m}\) behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \(2~\text{m/s}^2 \) and the car has acceleration \(4~\text{m/s}^2. \) The car will catch up with the bus after a time of:
1. \(\sqrt{120}~\text{s} \)
2. \(15~\text{s}\)
3. \(10\sqrt2~\text{s} \)
4. \(\sqrt{110}~\text{s} \)
Subtopic:  Relative Motion in One Dimension |
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A train \(100~\text m\) long is moving with a velocity of \(40~\text{m/s}.\) It overtakes another train \(200~\text m\) long travelling in the same direction at \(30~\text{m/s}.\) How much time will the first train take to pass the second train completely?
1. \(30~\text s\) 
2. \(40~\text s\) 
3. \(50~\text s\) 
4. \(60~\text s\) 
Subtopic:  Relative Motion in One Dimension |
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A train 100 m long traveling at 40 m s-1 starts overtaking another train 200 m long traveling at 30 m s-1. The time taken by the first train to pass the second train completely is 

1. 30 s

2. 40 s

3. 50 s

4. 60 s

Subtopic:  Relative Motion in One Dimension |
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Two cars  and  start from a point at the same time in a straight line and their positions are represented by  and  At what time do the cars have the same velocity ? 

1. 

2. 

3. 

4. 

Subtopic:  Relative Motion in One Dimension |
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Two parallel rail tracks run north-south. Train A moves north with a speed of 54 kmh-1, and train B moves south with a speed of 90 kmh-1. The magnitude of the velocity of B with respect to A is:

1.  40 ms-1

2.  0 ms-1

3.  25 ms-1

4.  15 ms-1

 

Subtopic:  Relative Motion in One Dimension |
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A thief is running away on a straight road in a jeep moving with a speed of 9 m s-1. A policeman chases him on a motor cycle moving at a speed of 10 m s-1. If the instantaneous separation of the jeep from the motor cycle is 100 m, how long will it take for the policeman to catch the thief?

1. 1 s

2. 19 s

3. 90 s

4. 100 s

Subtopic:  Relative Motion in One Dimension |
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A bicycle traveling at speed \(v\) covers a distance \(\Delta x\) during a time interval \(\Delta t\). If a car travels at speed \(3v\), how much time does it take the car to go the same distance?
1. \(\Delta t+3\)
2. \(3 \Delta t\)
3. \(\frac{\Delta t}{3}\)
4. \(\Delta t - 3\)
Subtopic:  Relative Motion in One Dimension |
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Two particles move with constant speeds of \(3~\text{m/s}\) and \(5~\text{m/s}\) along the periphery of a square \(ABCD\) of side \(2~\text{m}\) (as shown). They start from \(A\) at the same time.

They meet for the first time:
1. at \(B\)
2. at \(C\)
3. between \(A\)\(B\)
4. between \(B\)\(C\)
Subtopic:  Relative Motion in One Dimension |
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At a metro station, a girl walks up a stationary escalator in time \(t_1\) . If she remains stationary on the escalator, then the escalator take her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be:
1. \(\left(t_1+t_2\right) / 2 \)
2. \(t_1 t_2 /\left(t_2-t_1\right) \)
3. \(t_1 t_2 /\left(t_2+t_1\right) \)
4. \(t_1-t_2\)
Subtopic:  Relative Motion in One Dimension |
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A bus is moving at a speed of \(10\) ms-1 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 speed should the scooterist chase the bus?
1. \(20\) ms-1
2. \(40\) ms-1
3. \(25\) ms-1
4. \(10\) ms-1
Subtopic:  Relative Motion in One Dimension |
 78%
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AIPMT - 2009
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