Q. No.A car is moving along east at \(10\) m/s and a bus is moving along north at \(10\) m/s. The velocity of the car with respect to the bus is along:
1.
North-East
2.
South-East
3.
North-West
4.
South-West
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:
| 1. | Acceleration is zero at \(t=1\) sec. |
| 2. | Speed is zero at \(t=0\) sec. |
| 3. | Acceleration is always zero. |
| 4. | Speed is \(3\) m/s at \(t=1\) sec. |
It is raining at \(20\) m/s in still air. Now a wind starts blowing with speed \(10\) m/s in the north direction. If a cyclist starts moving at \(10\) m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:
1. \(20\) m/s
2. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s
River of width \(500\) m is flowing at a speed of \(10\) m/s. A swimmer can swim at a speed of \(10\) m/s in still water. If he starts swimming at an angle of \(120^{\circ}\) with the flow direction, then the distance he travels along the river while crossing the river is:
1. \(250~\text{m}\)
2. \(500\sqrt{3}~\text{m}\)
3. \(\frac{500}{\sqrt{3}}~\text{m}\)
4. \(500~\text{m}\)
Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |
Which of the following statements is incorrect?
| 1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
| 2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
| 3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
| 4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
A man is walking on a horizontal road with a speed of \(4\) km/h. Suddenly, the rain starts vertically downwards with a speed of \(7\) km/h. The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}\) km/h
2. \(\sqrt{65}\) km/h
3. \(8\) km/h
4. \(4\) km/h
If a body is accelerating, then:
| 1. | it must speed up. |
| 2. | it may move at the same speed. |
| 3. | it may move with the same velocity. |
| 4. | it must slow down. |
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