01. Speed, Velocity and Acceleration
Motion in One Dimensions

141488 A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity = \(10 \mathrm{~ms}^{-2}\) )

1 \(4 \mathrm{~J}\)
2 \(60 \mathrm{~J}\)
3 \(64 \mathrm{~J}\)
4 \(8 \mathrm{~J}\)
Motion in One Dimensions

141489 A stone is released from an aeroplane which is rising with upward acceleration \(5 \mathrm{~m} / \mathrm{s}^{2}\). Here, g \(=10 \mathrm{~m} / \mathrm{s}^{2}\). Two seconds after the release, separation between stone and aeroplane will be

1 \(10 \mathrm{~m}\)
2 \(20 \mathrm{~m}\)
3 \(30 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141490 Two childrens Ramesh (on path ARB) and Sohan (on path ASB), travel down slides of identical height \(h\) but different shapes as shown in the figure. Assuming, they start down the frictionless slides at the same time with zero initial velocity, which of the following statement is true?
original image

1 Ramesh reaches the bottom first with the same average velocity as Sohan.
2 Ramesh reaches the bottom first with a larger average acceleration than Sohan.
3 Ramesh reaches the bottom first with the same average acceleration as Sohan.
4 They reach the bottom at same time with the same average acceleration.
Motion in One Dimensions

141492 A cart of mass \(150 \mathrm{~kg}\) is pulled horizontally on a frictionless surface with force \(10 \mathrm{~N}\). If \(100 \mathrm{~g} / \mathrm{s}\) sand is being dropped in the cart vertically then find the speed of the system when cart has \(100 \mathrm{~kg}\) sand in it.

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(50 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141493 The position vector of the particle is \(r(t)=a\) \(\cos \omega t \hat{\mathbf{i}}+\mathbf{a} \sin \omega t \hat{\mathbf{j}}\), where a and \(\omega\) are real constants of suitable dimensions. The acceleration is:

1 Perpendicular to the velocity
2 Parallel to the velocity
3 Directed away from the origin
4 Perpendicular to the position vector
5 Always along the direction of \(\hat{i}\)
Motion in One Dimensions

141488 A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity = \(10 \mathrm{~ms}^{-2}\) )

1 \(4 \mathrm{~J}\)
2 \(60 \mathrm{~J}\)
3 \(64 \mathrm{~J}\)
4 \(8 \mathrm{~J}\)
Motion in One Dimensions

141489 A stone is released from an aeroplane which is rising with upward acceleration \(5 \mathrm{~m} / \mathrm{s}^{2}\). Here, g \(=10 \mathrm{~m} / \mathrm{s}^{2}\). Two seconds after the release, separation between stone and aeroplane will be

1 \(10 \mathrm{~m}\)
2 \(20 \mathrm{~m}\)
3 \(30 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141490 Two childrens Ramesh (on path ARB) and Sohan (on path ASB), travel down slides of identical height \(h\) but different shapes as shown in the figure. Assuming, they start down the frictionless slides at the same time with zero initial velocity, which of the following statement is true?
original image

1 Ramesh reaches the bottom first with the same average velocity as Sohan.
2 Ramesh reaches the bottom first with a larger average acceleration than Sohan.
3 Ramesh reaches the bottom first with the same average acceleration as Sohan.
4 They reach the bottom at same time with the same average acceleration.
Motion in One Dimensions

141492 A cart of mass \(150 \mathrm{~kg}\) is pulled horizontally on a frictionless surface with force \(10 \mathrm{~N}\). If \(100 \mathrm{~g} / \mathrm{s}\) sand is being dropped in the cart vertically then find the speed of the system when cart has \(100 \mathrm{~kg}\) sand in it.

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(50 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141493 The position vector of the particle is \(r(t)=a\) \(\cos \omega t \hat{\mathbf{i}}+\mathbf{a} \sin \omega t \hat{\mathbf{j}}\), where a and \(\omega\) are real constants of suitable dimensions. The acceleration is:

1 Perpendicular to the velocity
2 Parallel to the velocity
3 Directed away from the origin
4 Perpendicular to the position vector
5 Always along the direction of \(\hat{i}\)
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Motion in One Dimensions

141488 A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity = \(10 \mathrm{~ms}^{-2}\) )

1 \(4 \mathrm{~J}\)
2 \(60 \mathrm{~J}\)
3 \(64 \mathrm{~J}\)
4 \(8 \mathrm{~J}\)
Motion in One Dimensions

141489 A stone is released from an aeroplane which is rising with upward acceleration \(5 \mathrm{~m} / \mathrm{s}^{2}\). Here, g \(=10 \mathrm{~m} / \mathrm{s}^{2}\). Two seconds after the release, separation between stone and aeroplane will be

1 \(10 \mathrm{~m}\)
2 \(20 \mathrm{~m}\)
3 \(30 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141490 Two childrens Ramesh (on path ARB) and Sohan (on path ASB), travel down slides of identical height \(h\) but different shapes as shown in the figure. Assuming, they start down the frictionless slides at the same time with zero initial velocity, which of the following statement is true?
original image

1 Ramesh reaches the bottom first with the same average velocity as Sohan.
2 Ramesh reaches the bottom first with a larger average acceleration than Sohan.
3 Ramesh reaches the bottom first with the same average acceleration as Sohan.
4 They reach the bottom at same time with the same average acceleration.
Motion in One Dimensions

141492 A cart of mass \(150 \mathrm{~kg}\) is pulled horizontally on a frictionless surface with force \(10 \mathrm{~N}\). If \(100 \mathrm{~g} / \mathrm{s}\) sand is being dropped in the cart vertically then find the speed of the system when cart has \(100 \mathrm{~kg}\) sand in it.

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(50 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141493 The position vector of the particle is \(r(t)=a\) \(\cos \omega t \hat{\mathbf{i}}+\mathbf{a} \sin \omega t \hat{\mathbf{j}}\), where a and \(\omega\) are real constants of suitable dimensions. The acceleration is:

1 Perpendicular to the velocity
2 Parallel to the velocity
3 Directed away from the origin
4 Perpendicular to the position vector
5 Always along the direction of \(\hat{i}\)
Motion in One Dimensions

141488 A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity = \(10 \mathrm{~ms}^{-2}\) )

1 \(4 \mathrm{~J}\)
2 \(60 \mathrm{~J}\)
3 \(64 \mathrm{~J}\)
4 \(8 \mathrm{~J}\)
Motion in One Dimensions

141489 A stone is released from an aeroplane which is rising with upward acceleration \(5 \mathrm{~m} / \mathrm{s}^{2}\). Here, g \(=10 \mathrm{~m} / \mathrm{s}^{2}\). Two seconds after the release, separation between stone and aeroplane will be

1 \(10 \mathrm{~m}\)
2 \(20 \mathrm{~m}\)
3 \(30 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141490 Two childrens Ramesh (on path ARB) and Sohan (on path ASB), travel down slides of identical height \(h\) but different shapes as shown in the figure. Assuming, they start down the frictionless slides at the same time with zero initial velocity, which of the following statement is true?
original image

1 Ramesh reaches the bottom first with the same average velocity as Sohan.
2 Ramesh reaches the bottom first with a larger average acceleration than Sohan.
3 Ramesh reaches the bottom first with the same average acceleration as Sohan.
4 They reach the bottom at same time with the same average acceleration.
Motion in One Dimensions

141492 A cart of mass \(150 \mathrm{~kg}\) is pulled horizontally on a frictionless surface with force \(10 \mathrm{~N}\). If \(100 \mathrm{~g} / \mathrm{s}\) sand is being dropped in the cart vertically then find the speed of the system when cart has \(100 \mathrm{~kg}\) sand in it.

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(50 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141493 The position vector of the particle is \(r(t)=a\) \(\cos \omega t \hat{\mathbf{i}}+\mathbf{a} \sin \omega t \hat{\mathbf{j}}\), where a and \(\omega\) are real constants of suitable dimensions. The acceleration is:

1 Perpendicular to the velocity
2 Parallel to the velocity
3 Directed away from the origin
4 Perpendicular to the position vector
5 Always along the direction of \(\hat{i}\)
Motion in One Dimensions

141488 A body of mass \(2 \mathrm{~kg}\) thrown vertically from the ground with a velocity of \(8 \mathrm{~ms}^{-1}\) reaches a maximum height \(3 \mathrm{~m}\). The work done by the air resistance is (acceleration due to gravity = \(10 \mathrm{~ms}^{-2}\) )

1 \(4 \mathrm{~J}\)
2 \(60 \mathrm{~J}\)
3 \(64 \mathrm{~J}\)
4 \(8 \mathrm{~J}\)
Motion in One Dimensions

141489 A stone is released from an aeroplane which is rising with upward acceleration \(5 \mathrm{~m} / \mathrm{s}^{2}\). Here, g \(=10 \mathrm{~m} / \mathrm{s}^{2}\). Two seconds after the release, separation between stone and aeroplane will be

1 \(10 \mathrm{~m}\)
2 \(20 \mathrm{~m}\)
3 \(30 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141490 Two childrens Ramesh (on path ARB) and Sohan (on path ASB), travel down slides of identical height \(h\) but different shapes as shown in the figure. Assuming, they start down the frictionless slides at the same time with zero initial velocity, which of the following statement is true?
original image

1 Ramesh reaches the bottom first with the same average velocity as Sohan.
2 Ramesh reaches the bottom first with a larger average acceleration than Sohan.
3 Ramesh reaches the bottom first with the same average acceleration as Sohan.
4 They reach the bottom at same time with the same average acceleration.
Motion in One Dimensions

141492 A cart of mass \(150 \mathrm{~kg}\) is pulled horizontally on a frictionless surface with force \(10 \mathrm{~N}\). If \(100 \mathrm{~g} / \mathrm{s}\) sand is being dropped in the cart vertically then find the speed of the system when cart has \(100 \mathrm{~kg}\) sand in it.

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(40 \mathrm{~m} / \mathrm{s}\)
4 \(50 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141493 The position vector of the particle is \(r(t)=a\) \(\cos \omega t \hat{\mathbf{i}}+\mathbf{a} \sin \omega t \hat{\mathbf{j}}\), where a and \(\omega\) are real constants of suitable dimensions. The acceleration is:

1 Perpendicular to the velocity
2 Parallel to the velocity
3 Directed away from the origin
4 Perpendicular to the position vector
5 Always along the direction of \(\hat{i}\)