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.
In the following velocity-time graph of a body, the distance and displacement traveled by the body in 5 seconds in metres will be, respectively:
1. 75, 115
2. 110, 70
3. 45, 75
4. 95, 55
Figure below shows the velocity-time graph. This graph tells us that the body is:
1. Starting from rest and moving with increasing acceleration
2. Moving with uniform speed.
3. Moving with uniform acceleration.
4. Moving with decreasing acceleration.
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 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. | \(x>0, v>0, a<0\) |
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)
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