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Q. No.A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The average velocity of the ball during the motion is (downward):
1.
\(\large\frac{v_2-v_1}{2}\)
2.
\(\large\frac{v_2+v_1}{2}\)
3.
\({v_2-v_1}\)
4.
\({v_2+v_1}\)
Subtopic: Average Speed & Average Velocity |
From NCERT
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A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The acceleration of the ball is (downward):
The acceleration of the ball is (downward):
| 1. | \(\dfrac{v_2-v_1}{t_2-t_1}\) | 2. | \(\dfrac{v_2+v_1}{t_2-t_1}\) |
| 3. | \(\dfrac{v_2-v_1}{t_2+t_1}\) | 4. | \(\dfrac{v_2+v_1}{t_2+t_1}\) |
Subtopic: Acceleration |
From NCERT
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The line \(AB\) makes a \(45^\circ\) angle with the \(x\)-axis, but it moves along the negative \(y\)-axis with a speed of \(1~\text{m/s}.\) The velocity, of the intersection \((C)\) of \(AB\) with \(x\)-axis, is:
| 1. | \(1~\text{m/s}\) along the positive \(x\)-axis |
| 2. | \(1~\text{m/s}\) along the negative \(x\)-axis |
| 3. | \(\dfrac{1}{\sqrt2} ~\text{m/s}\) along the positive \(x\)-axis |
| 4. | \(\dfrac{1}{\sqrt2}~\text{m/s}\) along the negative \(x\)-axis |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
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Given below are two statements:
| Statement I: | If the displacement of a particle varies quadratically as the time elapsed, the particle moves with a constant acceleration. |
| Statement II: | The distance travelled by a particle is always greater than or equal to the magnitude of the displacement. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Distance & Displacement |
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From NCERT
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Consider a chessboard, as shown in the figure, where the width of each square is \(2~\text{cm}.\) Assume that all pieces are kept at the centres of the squares, before and after a move. Also, assume that each single move takes \(2~\text{s}\) – irrespective of however many squares (distance) are taken.
What is the maximum possible displacement of a rook \(\Large(♖)\) in a single move?
Note: A rook can move any number of squares along only \(x\) or only \(y\) (positive or negative) direction.
What is the maximum possible displacement of a rook \(\Large(♖)\) in a single move?
Note: A rook can move any number of squares along only \(x\) or only \(y\) (positive or negative) direction.
| 1. | \(14~\text{cm}\) | 2. | \(16~\text{cm}\) |
| 3. | \(18~\text{cm}\) | 4. | \(16\sqrt2~\text{cm}\) |
Subtopic: Distance & Displacement |
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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.
Their average accelerations, over the motion till they meet for the first time, are:
Their average accelerations, over the motion till they meet for the first time, are:
| 1. | \(3\sqrt2~\text{m/s}^2,5\sqrt2~\text{m/s}^2 \) |
| 2. | \(3~\text{m/s}^2,5~\text{m/s}^2 \) |
| 3. | \(3\sqrt2~\text{m/s}^2,10~\text{m/s}^2 \) |
| 4. | \(6~\text{m/s}^2,10~\text{m/s}^2 \) |
Subtopic: Acceleration |
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Two particles \(A\) & \(B\) start moving from the same point with initial velocities and accelerations:
The vector \(\overrightarrow{AB}\) is given by:
1. \(2\vec ut+{\large\frac12}\vec at^2\)
2. \(2\vec ut-{\large\frac12}\vec at^2\)
3. \({\large\frac12}\vec at^2\)
4. \(-{\large\frac12}\vec at^2\)
| Particles\(\rightarrow\) | \(A\) | \(B\) |
| initial velocity | \(-\vec u\) | \(\vec u\) |
| acceleration | \(\vec a\) | zero |
The vector \(\overrightarrow{AB}\) is given by:
1. \(2\vec ut+{\large\frac12}\vec at^2\)
2. \(2\vec ut-{\large\frac12}\vec at^2\)
3. \({\large\frac12}\vec at^2\)
4. \(-{\large\frac12}\vec at^2\)
Subtopic: Uniformly Accelerated Motion |
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From NCERT
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An athlete runs along a straight track. She begins from rest and accelerates uniformly for \(2~\text{s},\) reaching a speed of \(9~\text{m/s}.\) She then runs at this constant speed for a certain duration before decelerating uniformly to rest. The total time from start to finish is \(12~\text s.\) If her acceleration during the first phase is exactly twice the magnitude of her deceleration during the last phase, what is the total distance she covers during the entire motion?
1. \(81~\text{m}\)
2. \(108~\text{m}\)
3. \(90~\text{m}\)
4. \(72~\text{m}\)
1. \(81~\text{m}\)
2. \(108~\text{m}\)
3. \(90~\text{m}\)
4. \(72~\text{m}\)
Subtopic: Distance & Displacement |
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From NCERT
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A ball is thrown vertically upwards with a velocity of \(19.6~\text{ms}^{-1}\) from the top of a tower. The ball strikes the ground after \(6~\text s/.\) The height from the ground up to which the ball can rise will be \(\dfrac{k}{5}~\text m.\) m. The value of \(k:\)
(use \(g=9.8~\text{ms}^{-2})\)
1. \(392 \)
2. \(360\)
3. \(315\)
4. \(420\)
(use \(g=9.8~\text{ms}^{-2})\)
1. \(392 \)
2. \(360\)
3. \(315\)
4. \(420\)
Subtopic: Uniformly Accelerated Motion |
60%
From NCERT
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A bullet is shot vertically downwards with an initial velocity of \(100\) m/s from a certain height. Within \(10\) s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time \(t=20\) s will be : (Take \(g=10\) m/s2 )
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Graphs |
From NCERT
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