02. Relative Velocity in One Dimension
Motion in One Dimensions

141666 A car travelling at \(15 \mathrm{~m} / \mathrm{s}\) overtake another car travelling at \(10 \mathrm{~m} / \mathrm{s}\). Assuming, each car is \(4 \mathrm{~m}\) long. What is the time taken during the overtake?

1 \(1.6 \mathrm{~s}\)
2 \(0.8 \mathrm{~s}\)
3 \(0.6 \mathrm{~s}\)
4 \(0.4 \mathrm{~s}\)
Motion in One Dimensions

141667 Two buses \(A\) and \(B\) are moving in opposite direction. Now if the first bus \(A\) moves towards east with a speed of \(36 \mathrm{~km} / \mathrm{h}\) and bus \(B\) moves towards west with a speed of \(18 \mathrm{~km} / \mathrm{h}\), then the bus \(B\) appears to bus \(A\) as

1 moving with a speed of \(5 \mathrm{~m} / \mathrm{s}\) from east to west
2 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from west to east
3 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from east to west
4 moving with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from east to west
Motion in One Dimensions

141668 Trains \(A\) and \(B\) are running on parallel tracks in the opposite directions with speeds of 36 \(\mathrm{km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. A person is walking in train \(A\) in the opposite direction to its motion with a speed of \(1.8 \mathrm{~km} / \mathrm{h}\). Speed (in \(\mathrm{ms}^{-1}\) ) of this person as observed from train \(B\) will be close to (Take, the distance between the tracks as negligible)

1 28.5
2 30.5
3 29.5
4 31.5
Motion in One Dimensions

141669 Two particles 1 and 2 are allowed to descend on two frictionless chords \(O P\) and \(O Q\) as shown in the figure. The ratio of the speeds of the particles 1 and 2 , respectively when they reach the circumference is
original image

1 \(\frac{1}{2}\)
2 2
3 \(\frac{3}{2}\)
4 \(\frac{2}{3}\)
Motion in One Dimensions

141670 A passenger train of length \(60 \mathrm{~m}\) travels at a speed of \(80 \mathrm{~km} / \mathrm{hr}\). Another freight train of length \(120 \mathrm{~m}\) travels at a speed of \(30 \mathrm{~km} / \mathrm{hr}\). The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

1 \(\frac{3}{2}\)
2 \(\frac{25}{11}\)
3 \(\frac{11}{5}\)
4 \(\frac{5}{2}\)
Motion in One Dimensions

141666 A car travelling at \(15 \mathrm{~m} / \mathrm{s}\) overtake another car travelling at \(10 \mathrm{~m} / \mathrm{s}\). Assuming, each car is \(4 \mathrm{~m}\) long. What is the time taken during the overtake?

1 \(1.6 \mathrm{~s}\)
2 \(0.8 \mathrm{~s}\)
3 \(0.6 \mathrm{~s}\)
4 \(0.4 \mathrm{~s}\)
Motion in One Dimensions

141667 Two buses \(A\) and \(B\) are moving in opposite direction. Now if the first bus \(A\) moves towards east with a speed of \(36 \mathrm{~km} / \mathrm{h}\) and bus \(B\) moves towards west with a speed of \(18 \mathrm{~km} / \mathrm{h}\), then the bus \(B\) appears to bus \(A\) as

1 moving with a speed of \(5 \mathrm{~m} / \mathrm{s}\) from east to west
2 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from west to east
3 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from east to west
4 moving with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from east to west
Motion in One Dimensions

141668 Trains \(A\) and \(B\) are running on parallel tracks in the opposite directions with speeds of 36 \(\mathrm{km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. A person is walking in train \(A\) in the opposite direction to its motion with a speed of \(1.8 \mathrm{~km} / \mathrm{h}\). Speed (in \(\mathrm{ms}^{-1}\) ) of this person as observed from train \(B\) will be close to (Take, the distance between the tracks as negligible)

1 28.5
2 30.5
3 29.5
4 31.5
Motion in One Dimensions

141669 Two particles 1 and 2 are allowed to descend on two frictionless chords \(O P\) and \(O Q\) as shown in the figure. The ratio of the speeds of the particles 1 and 2 , respectively when they reach the circumference is
original image

1 \(\frac{1}{2}\)
2 2
3 \(\frac{3}{2}\)
4 \(\frac{2}{3}\)
Motion in One Dimensions

141670 A passenger train of length \(60 \mathrm{~m}\) travels at a speed of \(80 \mathrm{~km} / \mathrm{hr}\). Another freight train of length \(120 \mathrm{~m}\) travels at a speed of \(30 \mathrm{~km} / \mathrm{hr}\). The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

1 \(\frac{3}{2}\)
2 \(\frac{25}{11}\)
3 \(\frac{11}{5}\)
4 \(\frac{5}{2}\)
Motion in One Dimensions

141666 A car travelling at \(15 \mathrm{~m} / \mathrm{s}\) overtake another car travelling at \(10 \mathrm{~m} / \mathrm{s}\). Assuming, each car is \(4 \mathrm{~m}\) long. What is the time taken during the overtake?

1 \(1.6 \mathrm{~s}\)
2 \(0.8 \mathrm{~s}\)
3 \(0.6 \mathrm{~s}\)
4 \(0.4 \mathrm{~s}\)
Motion in One Dimensions

141667 Two buses \(A\) and \(B\) are moving in opposite direction. Now if the first bus \(A\) moves towards east with a speed of \(36 \mathrm{~km} / \mathrm{h}\) and bus \(B\) moves towards west with a speed of \(18 \mathrm{~km} / \mathrm{h}\), then the bus \(B\) appears to bus \(A\) as

1 moving with a speed of \(5 \mathrm{~m} / \mathrm{s}\) from east to west
2 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from west to east
3 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from east to west
4 moving with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from east to west
Motion in One Dimensions

141668 Trains \(A\) and \(B\) are running on parallel tracks in the opposite directions with speeds of 36 \(\mathrm{km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. A person is walking in train \(A\) in the opposite direction to its motion with a speed of \(1.8 \mathrm{~km} / \mathrm{h}\). Speed (in \(\mathrm{ms}^{-1}\) ) of this person as observed from train \(B\) will be close to (Take, the distance between the tracks as negligible)

1 28.5
2 30.5
3 29.5
4 31.5
Motion in One Dimensions

141669 Two particles 1 and 2 are allowed to descend on two frictionless chords \(O P\) and \(O Q\) as shown in the figure. The ratio of the speeds of the particles 1 and 2 , respectively when they reach the circumference is
original image

1 \(\frac{1}{2}\)
2 2
3 \(\frac{3}{2}\)
4 \(\frac{2}{3}\)
Motion in One Dimensions

141670 A passenger train of length \(60 \mathrm{~m}\) travels at a speed of \(80 \mathrm{~km} / \mathrm{hr}\). Another freight train of length \(120 \mathrm{~m}\) travels at a speed of \(30 \mathrm{~km} / \mathrm{hr}\). The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

1 \(\frac{3}{2}\)
2 \(\frac{25}{11}\)
3 \(\frac{11}{5}\)
4 \(\frac{5}{2}\)
Motion in One Dimensions

141666 A car travelling at \(15 \mathrm{~m} / \mathrm{s}\) overtake another car travelling at \(10 \mathrm{~m} / \mathrm{s}\). Assuming, each car is \(4 \mathrm{~m}\) long. What is the time taken during the overtake?

1 \(1.6 \mathrm{~s}\)
2 \(0.8 \mathrm{~s}\)
3 \(0.6 \mathrm{~s}\)
4 \(0.4 \mathrm{~s}\)
Motion in One Dimensions

141667 Two buses \(A\) and \(B\) are moving in opposite direction. Now if the first bus \(A\) moves towards east with a speed of \(36 \mathrm{~km} / \mathrm{h}\) and bus \(B\) moves towards west with a speed of \(18 \mathrm{~km} / \mathrm{h}\), then the bus \(B\) appears to bus \(A\) as

1 moving with a speed of \(5 \mathrm{~m} / \mathrm{s}\) from east to west
2 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from west to east
3 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from east to west
4 moving with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from east to west
Motion in One Dimensions

141668 Trains \(A\) and \(B\) are running on parallel tracks in the opposite directions with speeds of 36 \(\mathrm{km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. A person is walking in train \(A\) in the opposite direction to its motion with a speed of \(1.8 \mathrm{~km} / \mathrm{h}\). Speed (in \(\mathrm{ms}^{-1}\) ) of this person as observed from train \(B\) will be close to (Take, the distance between the tracks as negligible)

1 28.5
2 30.5
3 29.5
4 31.5
Motion in One Dimensions

141669 Two particles 1 and 2 are allowed to descend on two frictionless chords \(O P\) and \(O Q\) as shown in the figure. The ratio of the speeds of the particles 1 and 2 , respectively when they reach the circumference is
original image

1 \(\frac{1}{2}\)
2 2
3 \(\frac{3}{2}\)
4 \(\frac{2}{3}\)
Motion in One Dimensions

141670 A passenger train of length \(60 \mathrm{~m}\) travels at a speed of \(80 \mathrm{~km} / \mathrm{hr}\). Another freight train of length \(120 \mathrm{~m}\) travels at a speed of \(30 \mathrm{~km} / \mathrm{hr}\). The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

1 \(\frac{3}{2}\)
2 \(\frac{25}{11}\)
3 \(\frac{11}{5}\)
4 \(\frac{5}{2}\)
Motion in One Dimensions

141666 A car travelling at \(15 \mathrm{~m} / \mathrm{s}\) overtake another car travelling at \(10 \mathrm{~m} / \mathrm{s}\). Assuming, each car is \(4 \mathrm{~m}\) long. What is the time taken during the overtake?

1 \(1.6 \mathrm{~s}\)
2 \(0.8 \mathrm{~s}\)
3 \(0.6 \mathrm{~s}\)
4 \(0.4 \mathrm{~s}\)
Motion in One Dimensions

141667 Two buses \(A\) and \(B\) are moving in opposite direction. Now if the first bus \(A\) moves towards east with a speed of \(36 \mathrm{~km} / \mathrm{h}\) and bus \(B\) moves towards west with a speed of \(18 \mathrm{~km} / \mathrm{h}\), then the bus \(B\) appears to bus \(A\) as

1 moving with a speed of \(5 \mathrm{~m} / \mathrm{s}\) from east to west
2 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from west to east
3 moving with a speed of \(15 \mathrm{~m} / \mathrm{s}\) from east to west
4 moving with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from east to west
Motion in One Dimensions

141668 Trains \(A\) and \(B\) are running on parallel tracks in the opposite directions with speeds of 36 \(\mathrm{km} / \mathrm{h}\) and \(72 \mathrm{~km} / \mathrm{h}\), respectively. A person is walking in train \(A\) in the opposite direction to its motion with a speed of \(1.8 \mathrm{~km} / \mathrm{h}\). Speed (in \(\mathrm{ms}^{-1}\) ) of this person as observed from train \(B\) will be close to (Take, the distance between the tracks as negligible)

1 28.5
2 30.5
3 29.5
4 31.5
Motion in One Dimensions

141669 Two particles 1 and 2 are allowed to descend on two frictionless chords \(O P\) and \(O Q\) as shown in the figure. The ratio of the speeds of the particles 1 and 2 , respectively when they reach the circumference is
original image

1 \(\frac{1}{2}\)
2 2
3 \(\frac{3}{2}\)
4 \(\frac{2}{3}\)
Motion in One Dimensions

141670 A passenger train of length \(60 \mathrm{~m}\) travels at a speed of \(80 \mathrm{~km} / \mathrm{hr}\). Another freight train of length \(120 \mathrm{~m}\) travels at a speed of \(30 \mathrm{~km} / \mathrm{hr}\). The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

1 \(\frac{3}{2}\)
2 \(\frac{25}{11}\)
3 \(\frac{11}{5}\)
4 \(\frac{5}{2}\)