Q. No.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. \(\frac{L \left(\right. v_{1} + v_{2} \left.\right)}{v_{1} v_{2}}\)
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. \(\frac{L \left(\right. v_{1} + v_{2} \left.\right)}{v_{1} v_{2}}\)
The variation of quantity \(A\) with quantity \(B\) is plotted in the given figure which describes the motion of a particle in a straight line.
Consider the following statements:
| 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. |
Select the correct option:
1. (a, b, c)
2. (b, c, d)
3. (a, c, d)
4. (a, c)
A ball is bouncing elastically with a speed of \(1\) m/s between the walls of a railway compartment of size \(10\) m in a direction perpendicular to the walls. The train is moving at a constant velocity of \(10\) m/s parallel to the direction of motion of the ball. As seen from the ground:
| (a) | the direction of motion of the ball changes every \(10\) sec. |
| (b) | the speed of the ball changes every \(10\) sec. |
| (c) | the average speed of the ball over any \(20\) sec intervals is fixed. |
| (d) | the acceleration of the ball is the same as from the train. |
Choose the correct option:
| 1. | (a), (c), (d) | 2. | (a), (c) |
| 3. | (b), (c), (d) | 4. | (a), (b), (c) |
If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0\), then:
| 1. | the displacement in time \(T\) must always take non-negative values. |
| 2. | the displacement \(x\) in time \(T\) satisfies \(-{v_0T} \lt x \lt {v_0T}\). |
| 3. | the acceleration is always a non-negative number. |
| 4. | the motion has no turning points. |
A lift is coming from the \(8\)th floor and is just about to reach the \(4\)th floor. Taking the ground floor as the 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. | \(x>0, v>0, a<0\) |
Among the four graphs shown in the figure, there is only one graph for which average velocity over the time interval \((0,T)\) can vanish for a suitably chosen \(T\). Select the graph.
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A body is thrown upwards and reaches its maximum height. At that position:
| 1. | its velocity is zero and its acceleration is also zero. |
| 2. | its velocity is zero but its acceleration is maximum. |
| 3. | its acceleration is minimum. |
| 4. | its velocity is zero and its acceleration is the acceleration due to gravity. |
Two trains each of length \(100\) m are moving parallel towards each other at speeds \(72\) km/h and \(36\) km/h respectively. In how much time will they cross each other?
1. \(4.5~\text{s}\)
2. \(6.67~\text{s}\)
3. \(3.5~\text{s}\)
4. \(7.25~\text{s}\)
Which one of the following displacement-time graph represents two moving objects \(P\) and \(Q\) with zero relative velocity?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Two balls are projected upward simultaneously with speeds of \(40\) m/s and \(60\) m/s. The relative position \((x)\) of the second ball with respect to the first ball at time \(t=5\) s will be: (neglect air resistance)
1. \(20\) m
2. \(80\) m
3. \(100\) m
4. \(120\) m
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