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Q. No.Among the four graphs (Fig. 3.1), there is only one graph for which average velocity over the time intervel (0, T ) can vanish for a suitably chosen T. Which one is it?
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2. |  |
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4. |  |
Subtopic: Average Speed & Average Velocity |
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Level 3: 35%-60%
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A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?
1. \(x<0, v<0, a>0 \)
2. \(x>0, v<0, a<0 \)
3. \(x>0, v<0, a>0 \)
4. \(x>0, v>0, a<0\)
1. \(x<0, v<0, a>0 \)
2. \(x>0, v<0, a<0 \)
3. \(x>0, v<0, a>0 \)
4. \(x>0, v>0, a<0\)
Subtopic: Uniformly Accelerated Motion |
Level 3: 35%-60%
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In one dimensional motion, instantaneous speed \(v\) satisfies \(0 \leq v<v_o \text {. }\)
| 1. | The displacement in time T must always take non-negative values. |
| 2. | The displacement x in time T satisfies \(-v_0 \mathrm{~T}<x<v_0 \mathrm{~T} .\) |
| 3. | The acceleration is always a non-negative number. |
| 4. | The motion has no turning points. |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
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A vehicle travels half the distance L with speed \(V_1\) and the other half with speed \(V_2\), then its average speed is
1. \(\frac{V_1+V_2}{2} \)
2. \(\frac{2 V_1+V_2}{V_1+V_2} \)
3. \(\frac{2 V_1 V_2}{V_1+V_2} \)
4. \(\frac{L\left(V_1+V_2\right)}{V_1 V_2}\)
1. \(\frac{V_1+V_2}{2} \)
2. \(\frac{2 V_1+V_2}{V_1+V_2} \)
3. \(\frac{2 V_1 V_2}{V_1+V_2} \)
4. \(\frac{L\left(V_1+V_2\right)}{V_1 V_2}\)
Subtopic: Average Speed & Average Velocity |
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Level 1: 80%+
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The displacement of a particle is given by \(x=(t-2)^2\) where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is
1. 4 m
2. 8 m
3. 12 m
4. 16 m
1. 4 m
2. 8 m
3. 12 m
4. 16 m
Subtopic: Instantaneous Speed & Instantaneous Velocity |
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Level 2: 60%+
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At a metro station, a girl walks up a stationary escalator in time \(t_1\) . If she remains stationary on the escalator, then the escalator take her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be:
1. \(\left(t_1+t_2\right) / 2 \)
2. \(t_1 t_2 /\left(t_2-t_1\right) \)
3. \(t_1 t_2 /\left(t_2+t_1\right) \)
4. \(t_1-t_2\)
1. \(\left(t_1+t_2\right) / 2 \)
2. \(t_1 t_2 /\left(t_2-t_1\right) \)
3. \(t_1 t_2 /\left(t_2+t_1\right) \)
4. \(t_1-t_2\)
Subtopic: Relative Motion in One Dimension |
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Level 1: 80%+
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The variation of quantity \(A\) with quantity \(B\), plotted in Fig. 3.2 describes the motion of a particle in a straight line.
Choose the correct option:
1. (a), (c), (d)
2. (a) only
3. (b) only
4. (d) only
| (a) | Quantity \(B\) may represent time. |
| (b) | Quantity \(A\) is velocity if motion is uniform. |
| (c) | Quantity \(A\) is displacement if motion is uniform. |
| (d) | Quantity \(A\) is velocity if motion is uniformly accelerated. |
1. (a), (c), (d)
2. (a) only
3. (b) only
4. (d) only
Subtopic: Graphs |
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A graph of \(x\) versus \(t\) is shown in the figure. Choose correct alternatives from below.
Choose the correct option:
| (a) | The particle was released from rest at \(t = 0\). |
| (b) | At \(B,\) the acceleration \(a > 0\). |
| (c) | At \(C,\) the velocity and the acceleration vanish. |
| (d) | Average velocity for the motion between \(A\) and \(D\) is positive. |
| (e) | The speed at \(D\) exceeds that at \(E\). |
Choose the correct option:
| 1. | (b), (c), (d) | 2. | (a), (b), (c), (d) |
| 3. | (a), (d) | 4. | (a), (c), (e) |
Subtopic: Graphs |
Level 3: 35%-60%
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For the one-dimensional motion, described by \(x=t-\sin t\)
Choose the correct option:
| (a) | \(x(t)>0\) for all \(t>0\) |
| (b) | \(v(t)>0\) for all \(t>0\). |
| (c) | \(a(t)>0\) for all \(t>0\). |
| (d) | \(v(t)>0\) lies between \(0\) and \(2\). |
Choose the correct option:
| 1. | (b), (c) |
| 2. | (a), (b), (d) |
| 3. | (a), (d) |
| 4. | (b), (d) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
Level 3: 35%-60%
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Q. No.
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