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Q. No.The position of an object moving along the \(\mathrm x\)-axis is given by \(x = a+bt^{2}\) where \(a=10\) m, \(b=2\) ms-2 and \(t\) is in seconds. The velocity at \(t=3.0\) s is:
1. \(12\) ms-1
2. \(20\) ms-1
3. \(36\) ms-1
4. \(46\) ms-1
Subtopic: Instantaneous Speed & Instantaneous Velocity |
87%
Level 1: 80%+
Hints
Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line. Their positions are represented by \(X_p(t)=\alpha t+\beta t^2 \) and \(X_{Q}(t)=ft-t^2 \). At what time do both the buses have the same velocity?
| 1. | \(\dfrac{\alpha-f}{1+\beta} \) | 2. | \(\dfrac{\alpha+f}{2(\beta-1)} \) |
| 3. | \(\dfrac{\alpha+f}{2(1+\beta)} \) | 4. | \(\dfrac{f-\alpha}{2(1+\beta)}\) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
88%
Level 1: 80%+
Hints
A particle is thrown vertically upward. Its velocity at half of the height is \(10\) m/s, then the maximum height attained by it is: (\(g=10\) m/s2)
| 1. | \(8\) m | 2. | \(20\) m |
| 3. | \(10\) m | 4. | \(16\) m |
Subtopic: Uniformly Accelerated Motion |
80%
Level 1: 80%+
Hints
Given below are two statements:
| Assertion (A): | If the average velocity of a particle over a certain time interval is zero, it is possible that the instantaneous velocity of the particle is never zero during that interval. |
| Reason (R): | For a particle moving along a straight line, if its average velocity over a time interval is zero, then there must be at least one instant within that interval when the instantaneous velocity is zero. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Average Speed & Average Velocity |
Level 3: 35%-60%
Hints
Select the correct option based on the statements given below:
| Assertion (A): | A body can have acceleration even if its velocity is zero at a given instant of time. |
| Reason (R): | A body is momentarily at rest when it reverses its direction of motion. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Uniformly Accelerated Motion |
65%
Level 2: 60%+
Hints
Given below are two statements:
| Assertion (A): | A particle having zero acceleration must have a constant speed. |
| Reason (R): | A particle having constant speed must have zero acceleration. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Acceleration |
57%
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | Adding a scalar to a vector of the same dimension is a meaningful algebraic operation. |
| Reason (R): | Displacement can be added to distance. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Distance & Displacement |
73%
Level 2: 60%+
Hints
The displacement-time \((s\text-t)\) graphs of two moving particles \(A~\text{and}~B\) make angles of \(30^\circ\) and \(45^\circ\) with the \(x\text-\)axis as shown in the figure. The ratio of their respective velocity \(\left(\dfrac{v_A}{v_B}\right) \) is:
1. \(1: \sqrt{3}\)
2. \(\sqrt{3}: 1\)
3. \(1:1\)
4. \(1:2\)
1. \(1: \sqrt{3}\)
2. \(\sqrt{3}: 1\)
3. \(1:1\)
4. \(1:2\)
Subtopic: Graphs |
75%
Level 2: 60%+
NEET - 2022
Hints
A particle moving in unidirectional motion travels half of the total distance with a constant speed of \(15 \) m/s. Now the first half of the remaining journey time, it travels at \(10\) m/s, and the second half of the remaining journey time, it travels at \(5\) m/s. The average speed of the particle is:
1. \(12\) m/s
2. \(10\) m/s
3. \(7\) m/s
4. \(15\) m/s
1. \(12\) m/s
2. \(10\) m/s
3. \(7\) m/s
4. \(15\) m/s
Subtopic: Average Speed & Average Velocity |
78%
Level 2: 60%+
Hints
A particle is moving along a straight line such that its position depends on time as \(x=1-at+bt^{2} \), where \(a=2~\text{m/s}\), \(b=1~\text{m/s}^2\). The distance covered by the particle during the first \(3\) seconds from start of the motion will be:
| 1. | \(2~\text{m}\) | 2. | \(5~\text{m}\) |
| 3. | \(7~\text{m}\) | 4. | \(4~\text{m}\) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
Level 3: 35%-60%
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