02. Relative Velocity in One Dimension
Motion in One Dimensions

141657 A particle is moving on a circular path with a constant speed \(v\). It's change of velocity as it moves from \(A\) to \(B\) in the figure is-
original image

1 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
2 \(v \sin \theta\)
3 \(\frac{v \sin 2 \theta}{2}\)
4 \(2 \mathrm{v} \sin \theta\)
Motion in One Dimensions

141658 Particle \(A\) (which is located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant velocity \(1 \mathrm{~ms}^{-1}\). Another particle \(B\) is moving along the \(y\)-axis according to, \(y=c^{3}\); \(c=1 \mathrm{~ms}^{-1}\). Then the velocity of \(A\) relative to \(B\) at \(\mathbf{t}=\mathbf{1}\) is

1 \(\sqrt{10} \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(\sqrt{3} \mathrm{~ms}^{-1}\)
4 \(3 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141659 The variation of induced emf \((F)\) with time ( \(t\) ) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as
original image

1 original image
2 original image
3 original image
4 original image
Motion in One Dimensions

141660 Two cars \(A\) and \(B\) initially at rest are moving in same direction with accelerations \(a_{1}\) and \(a_{2}\) respectively. After a certain time, they achieve velocities \(v_{1}\) and \(v_{2}\) respectively and separated are by a distance of \(50 \mathrm{~m}\). If \(\left(a_{1}-a_{2}\right)=4 \mathrm{~m} / \mathrm{s}^{2}\), then the quantity \(\left(v_{1}-v_{2}\right)\) will be

1 \(24 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141657 A particle is moving on a circular path with a constant speed \(v\). It's change of velocity as it moves from \(A\) to \(B\) in the figure is-
original image

1 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
2 \(v \sin \theta\)
3 \(\frac{v \sin 2 \theta}{2}\)
4 \(2 \mathrm{v} \sin \theta\)
Motion in One Dimensions

141658 Particle \(A\) (which is located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant velocity \(1 \mathrm{~ms}^{-1}\). Another particle \(B\) is moving along the \(y\)-axis according to, \(y=c^{3}\); \(c=1 \mathrm{~ms}^{-1}\). Then the velocity of \(A\) relative to \(B\) at \(\mathbf{t}=\mathbf{1}\) is

1 \(\sqrt{10} \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(\sqrt{3} \mathrm{~ms}^{-1}\)
4 \(3 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141659 The variation of induced emf \((F)\) with time ( \(t\) ) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as
original image

1 original image
2 original image
3 original image
4 original image
Motion in One Dimensions

141660 Two cars \(A\) and \(B\) initially at rest are moving in same direction with accelerations \(a_{1}\) and \(a_{2}\) respectively. After a certain time, they achieve velocities \(v_{1}\) and \(v_{2}\) respectively and separated are by a distance of \(50 \mathrm{~m}\). If \(\left(a_{1}-a_{2}\right)=4 \mathrm{~m} / \mathrm{s}^{2}\), then the quantity \(\left(v_{1}-v_{2}\right)\) will be

1 \(24 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141657 A particle is moving on a circular path with a constant speed \(v\). It's change of velocity as it moves from \(A\) to \(B\) in the figure is-
original image

1 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
2 \(v \sin \theta\)
3 \(\frac{v \sin 2 \theta}{2}\)
4 \(2 \mathrm{v} \sin \theta\)
Motion in One Dimensions

141658 Particle \(A\) (which is located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant velocity \(1 \mathrm{~ms}^{-1}\). Another particle \(B\) is moving along the \(y\)-axis according to, \(y=c^{3}\); \(c=1 \mathrm{~ms}^{-1}\). Then the velocity of \(A\) relative to \(B\) at \(\mathbf{t}=\mathbf{1}\) is

1 \(\sqrt{10} \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(\sqrt{3} \mathrm{~ms}^{-1}\)
4 \(3 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141659 The variation of induced emf \((F)\) with time ( \(t\) ) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as
original image

1 original image
2 original image
3 original image
4 original image
Motion in One Dimensions

141660 Two cars \(A\) and \(B\) initially at rest are moving in same direction with accelerations \(a_{1}\) and \(a_{2}\) respectively. After a certain time, they achieve velocities \(v_{1}\) and \(v_{2}\) respectively and separated are by a distance of \(50 \mathrm{~m}\). If \(\left(a_{1}-a_{2}\right)=4 \mathrm{~m} / \mathrm{s}^{2}\), then the quantity \(\left(v_{1}-v_{2}\right)\) will be

1 \(24 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141657 A particle is moving on a circular path with a constant speed \(v\). It's change of velocity as it moves from \(A\) to \(B\) in the figure is-
original image

1 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
2 \(v \sin \theta\)
3 \(\frac{v \sin 2 \theta}{2}\)
4 \(2 \mathrm{v} \sin \theta\)
Motion in One Dimensions

141658 Particle \(A\) (which is located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant velocity \(1 \mathrm{~ms}^{-1}\). Another particle \(B\) is moving along the \(y\)-axis according to, \(y=c^{3}\); \(c=1 \mathrm{~ms}^{-1}\). Then the velocity of \(A\) relative to \(B\) at \(\mathbf{t}=\mathbf{1}\) is

1 \(\sqrt{10} \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(\sqrt{3} \mathrm{~ms}^{-1}\)
4 \(3 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141659 The variation of induced emf \((F)\) with time ( \(t\) ) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as
original image

1 original image
2 original image
3 original image
4 original image
Motion in One Dimensions

141660 Two cars \(A\) and \(B\) initially at rest are moving in same direction with accelerations \(a_{1}\) and \(a_{2}\) respectively. After a certain time, they achieve velocities \(v_{1}\) and \(v_{2}\) respectively and separated are by a distance of \(50 \mathrm{~m}\). If \(\left(a_{1}-a_{2}\right)=4 \mathrm{~m} / \mathrm{s}^{2}\), then the quantity \(\left(v_{1}-v_{2}\right)\) will be

1 \(24 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(12 \mathrm{~m} / \mathrm{s}\)