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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 |
58%
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%+
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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
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 |
79%
Level 2: 60%+
Hints
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
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 |
86%
Level 1: 80%+
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 |
72%
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. | \(1:2\) |
Subtopic: Graphs |
76%
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 |
77%
Level 2: 60%+
Hints
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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%
Hints
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