Q. No.The position of a particle at time \(t\) is given by, \(x=3t^3\), \(y=2t^2+8t\), and \(z=6t-5\). The initial velocity of the particle is:
1.
\(20\) unit
2.
\(10\) unit
3.
\(5\) unit
4.
\(13\) unit
A man can row a boat with a speed of \(10~\text{kmph}\) in still water. The river flows at \(6~\text{kmph}.\) If he crosses the river from one bank to the other along the shortest possible path, the time taken to cross the river of width \(1~\text{km}\) is:
1. \(\frac{1}{8}~\text{hr}\)
2. \(\frac{1}{4}~\text{hr}\)
3. \(\frac{1}{2}~\text{hr}\)
4. \(1~\text{hr}\)
A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:
| 1. | \(30~\text{kmph}\) towards \(\mathrm{W}\) |
| 2. | \(30~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
| 3. | \(42.4~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
| 4. | \(42.4~\text{kmph}\) towards \(\mathrm{N\text-W}\) |
Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)
| 1. | The faster one |
| 2. | The slower one |
| 3. | Depends on masses |
| 4. | Both will reach simultaneously |
A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. \(5\) unit
2. \(12\) unit
3. \(13\) unit
4. \(17\) unit
Which of the following is the angle between velocity and acceleration of a body in uniform circular motion?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)
A man is walking on a horizontal road at a speed of \(4~\text{km/hr}.\) Suddenly, the rain starts vertically downwards with a speed of \(7~\text{km/hr}.\) The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}~\text{km/hr}\)
2. \(\sqrt{65}~\text{km/hr}\)
3. \(8~\text{km/hr}\)
4. \(4~\text{km/hr}\)
A particle is moving in the \(XY\) plane such that \(x = \left(t^2 -2t\right)~\text m,\) and \(y = \left(2t^2-t\right)~\text m,\) then:
| 1. | the acceleration is zero at \(t=1~\text s.\) |
| 2. | the speed is zero at \(t=0~\text s.\) |
| 3. | the acceleration is always zero. |
| 4. | the speed is \(3~\text{m/s}\) at \(t=1~\text s.\) |
A particle is moving along a curve. Select the correct statement.
| 1. | If its speed is constant, then it has no acceleration. |
| 2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |
| 3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |
| 4. | If its speed is constant, its acceleration is perpendicular to its velocity. |
Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and the diameter \(AB.\) If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:
1. \(2\)
2. \(2\sqrt{3}\)
3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)
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