Q. No.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 vehicle travels half the distance \(L\) with speed \(v_1\) and the other half with speed \(v_2,\) then its average speed is:
| 1. | \(\dfrac{v_{1} + v_{2}}{2}\) | 2. | \(\dfrac{2 v_{1} + v_{2}}{v_{1} + v_{2}}\) |
| 3. | \(\dfrac{2 v_{1} v_{2}}{v_{1} + v_{2}}\) | 4. | \(\dfrac{L \left(\right. v_{1} + v_{2} \left.\right)}{v_{1} v_{2}}\) |
The displacement of a particle moving along a straight line is given by:
\(x = (t-2)^2,\)
where \(t\) is in seconds. What is the total distance travelled by the particle in the first \(4~\text{s}?\)
1. \(4~\text{m}\)
2. \(8~\text{m}\)
3. \(12~\text{m}\)
4. \(16~\text{m}\)
At a metro station, a girl walks up a stationary escalator in time \(t_1\)
1. \( \left(\mathrm{t}_1+\mathrm{t}_2\right) / 2\)
2. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_2-\mathrm{t}_1\right)\)
3. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_1+\mathrm{t}_2\right) \)
4. \( \mathrm{t}_1-\mathrm{t}_2\)
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 graph of \(x\) versus \(t\) is shown in the figure.
| (a) | The particle was released from rest at \(t = 0.\) |
| (b) | At \(B,\) the acceleration \(a > 0.\) |
| (c) | Average velocity for the motion between \(A\) and \(D\) is positive. |
| (d) | The speed at \(D\) exceeds that at \(E.\) |
Choose the correct alternatives:
1. (b, d)
2. (a, b)
3. (b, c)
4. (a, d)
| (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) | \(v(t)\) lies between \(0\) and \(2\) |
Choose the correct option:
1. (a), (c)
2. (b), (c)
3. (a), (d)
4. (b), (d)
A ball is bouncing elastically with a speed of \(1~\text{m/s}\) between the walls of a railway compartment of size \(10~\text m\) in a direction perpendicular to the walls. The train is moving at a constant velocity of \(10~\text{m/s}\) 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) |
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. |  |
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