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Q. No.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. \(\sqrt{110}~\text{s} \)
1. \(\sqrt{120}~\text{s} \)
2. \(15~\text{s}\)
3. \(10\sqrt2~\text{s} \)
4. \(\sqrt{110}~\text{s} \)
Subtopic: Â 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. \(60~\text s\)
1. \(30~\text s\)
2. \(40~\text s\)
3. \(50~\text s\)
4. \(60~\text s\)
Subtopic: Â Relative Motion in One Dimension |
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Two parallel rail tracks run north-south. Train \(A\) moves north with a speed of \(54\text{ km/h},\) and train \(B\) moves south with a speed of \(90\text{ km/h}.\) The magnitude of the velocity of \(B\) with respect to \(A\) is:
1. \(40\text{ m/s}\)
2. \(0\text{ m/s}\)
3. \(25\text{ m/s}\)
4. \(15\text{ m/s}\)
Subtopic: Â Relative Motion in One Dimension |
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Level 1: 80%+
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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. \(\dfrac{\Delta t}{3}\)
4. \(\Delta t - 3\)
1. \(\Delta t+3\)
2. \(3 \Delta t\)
3. \(\dfrac{\Delta t}{3}\)
4. \(\Delta t - 3\)
Subtopic: Â Relative Motion in One Dimension |
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Level 1: 80%+
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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 \(B\) & \(C\)
They meet for the first time:
1. at \(B\)
2. at \(C\)
3. between \(A\) & \(B\)
4. between \(B\) & \(C\)
Subtopic: Â Relative Motion in One Dimension |
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Level 2: 60%+
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