02. Relative Velocity in One Dimension
Motion in One Dimensions

141679 A ball \(A\) is thrown up vertically with a speed \(u\) and at the same instant another \(B\) is released from a height \(h\). At time \(t\), the speed of A relative to \(B\) is

1 \(\mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(\mathrm{u}-\mathrm{gt}\)
4 \(\sqrt{\left(u^{2}-g t\right)}\)
5 \(g t\)
Motion in One Dimensions

141680 Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed \(u\) along the track so that the relative velocities of the trains with respect to the wind are in the ratio \(1: 2\), then the speed of each train must be

1 \(3 \mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(5 \mathrm{u}\)
4 \(4 \mathrm{u}\)
5 \(\mathrm{u}\)
Motion in One Dimensions

141681 A \(500 \mathrm{~kg}\) boat is \(9 \mathrm{~m}\) long and is floating without motion on still water. A man of mass \(100 \mathrm{~kg}\) is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

1 \(1.5 \mathrm{~m}\) in the direction of displacement of the man
2 \(0.75 \mathrm{~m}\) in the direction of displacement of the man
3 \(1.5 \mathrm{~m}\) in the direction opposite to the displacement of the man
4 \(0.75 \mathrm{~m}\) in the direction opposite to the displacement of the man
Motion in One Dimensions

141682 A scooter going to the east at \(10 \mathrm{~m} / \mathrm{s}\) turns right through an angle of \(90^{\circ}\). If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is

1 \(20 \mathrm{~m} / \mathrm{s}\) in south-west direction
2 zero
3 \(10.0 \mathrm{~m} / \mathrm{s}\) in south direction
4 \(14.14 \mathrm{~m} / \mathrm{s}\) in south-western direction
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Motion in One Dimensions

141679 A ball \(A\) is thrown up vertically with a speed \(u\) and at the same instant another \(B\) is released from a height \(h\). At time \(t\), the speed of A relative to \(B\) is

1 \(\mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(\mathrm{u}-\mathrm{gt}\)
4 \(\sqrt{\left(u^{2}-g t\right)}\)
5 \(g t\)
Motion in One Dimensions

141680 Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed \(u\) along the track so that the relative velocities of the trains with respect to the wind are in the ratio \(1: 2\), then the speed of each train must be

1 \(3 \mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(5 \mathrm{u}\)
4 \(4 \mathrm{u}\)
5 \(\mathrm{u}\)
Motion in One Dimensions

141681 A \(500 \mathrm{~kg}\) boat is \(9 \mathrm{~m}\) long and is floating without motion on still water. A man of mass \(100 \mathrm{~kg}\) is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

1 \(1.5 \mathrm{~m}\) in the direction of displacement of the man
2 \(0.75 \mathrm{~m}\) in the direction of displacement of the man
3 \(1.5 \mathrm{~m}\) in the direction opposite to the displacement of the man
4 \(0.75 \mathrm{~m}\) in the direction opposite to the displacement of the man
Motion in One Dimensions

141682 A scooter going to the east at \(10 \mathrm{~m} / \mathrm{s}\) turns right through an angle of \(90^{\circ}\). If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is

1 \(20 \mathrm{~m} / \mathrm{s}\) in south-west direction
2 zero
3 \(10.0 \mathrm{~m} / \mathrm{s}\) in south direction
4 \(14.14 \mathrm{~m} / \mathrm{s}\) in south-western direction
Motion in One Dimensions

141679 A ball \(A\) is thrown up vertically with a speed \(u\) and at the same instant another \(B\) is released from a height \(h\). At time \(t\), the speed of A relative to \(B\) is

1 \(\mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(\mathrm{u}-\mathrm{gt}\)
4 \(\sqrt{\left(u^{2}-g t\right)}\)
5 \(g t\)
Motion in One Dimensions

141680 Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed \(u\) along the track so that the relative velocities of the trains with respect to the wind are in the ratio \(1: 2\), then the speed of each train must be

1 \(3 \mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(5 \mathrm{u}\)
4 \(4 \mathrm{u}\)
5 \(\mathrm{u}\)
Motion in One Dimensions

141681 A \(500 \mathrm{~kg}\) boat is \(9 \mathrm{~m}\) long and is floating without motion on still water. A man of mass \(100 \mathrm{~kg}\) is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

1 \(1.5 \mathrm{~m}\) in the direction of displacement of the man
2 \(0.75 \mathrm{~m}\) in the direction of displacement of the man
3 \(1.5 \mathrm{~m}\) in the direction opposite to the displacement of the man
4 \(0.75 \mathrm{~m}\) in the direction opposite to the displacement of the man
Motion in One Dimensions

141682 A scooter going to the east at \(10 \mathrm{~m} / \mathrm{s}\) turns right through an angle of \(90^{\circ}\). If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is

1 \(20 \mathrm{~m} / \mathrm{s}\) in south-west direction
2 zero
3 \(10.0 \mathrm{~m} / \mathrm{s}\) in south direction
4 \(14.14 \mathrm{~m} / \mathrm{s}\) in south-western direction
Motion in One Dimensions

141679 A ball \(A\) is thrown up vertically with a speed \(u\) and at the same instant another \(B\) is released from a height \(h\). At time \(t\), the speed of A relative to \(B\) is

1 \(\mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(\mathrm{u}-\mathrm{gt}\)
4 \(\sqrt{\left(u^{2}-g t\right)}\)
5 \(g t\)
Motion in One Dimensions

141680 Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed \(u\) along the track so that the relative velocities of the trains with respect to the wind are in the ratio \(1: 2\), then the speed of each train must be

1 \(3 \mathrm{u}\)
2 \(2 \mathrm{u}\)
3 \(5 \mathrm{u}\)
4 \(4 \mathrm{u}\)
5 \(\mathrm{u}\)
Motion in One Dimensions

141681 A \(500 \mathrm{~kg}\) boat is \(9 \mathrm{~m}\) long and is floating without motion on still water. A man of mass \(100 \mathrm{~kg}\) is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

1 \(1.5 \mathrm{~m}\) in the direction of displacement of the man
2 \(0.75 \mathrm{~m}\) in the direction of displacement of the man
3 \(1.5 \mathrm{~m}\) in the direction opposite to the displacement of the man
4 \(0.75 \mathrm{~m}\) in the direction opposite to the displacement of the man
Motion in One Dimensions

141682 A scooter going to the east at \(10 \mathrm{~m} / \mathrm{s}\) turns right through an angle of \(90^{\circ}\). If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is

1 \(20 \mathrm{~m} / \mathrm{s}\) in south-west direction
2 zero
3 \(10.0 \mathrm{~m} / \mathrm{s}\) in south direction
4 \(14.14 \mathrm{~m} / \mathrm{s}\) in south-western direction