An aeroplane flies $$400$$ m north and then $$300$$ m west and then flies $$1200$$ m upwards. Its net displacement is: 1.  $$1200$$ m 2.  $$1300$$ m 3.  $$1400$$ m 4.  $$1500$$ m

Subtopic:  Position & Displacement |
74%
From NCERT
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Select the incorrect statement:

 1 It is possible to have $$\left|\frac{{d} \overrightarrow{v}}{dt}\right| = 0$$ and $$\frac{{d}|\overrightarrow{v}|}{{dt}} \neq 0$$ 2 It is possible to have$$\left|\frac{{d} \overrightarrow{{v}}}{{dt}}\right| \neq 0$$ and $$\frac{{d}|\overrightarrow{{v}}|}{dt}=0 .$$ 3 it is possible to have$$\left|\frac{{d} \overrightarrow{v}}{{dt}}\right|=0$$ and $$\frac{{d}|\overrightarrow{{v}}|}{dt}=0 .$$ 4 It is possible to have $$\left|\frac{{d} \overrightarrow{{v}}}{{dt}}\right| \neq 0$$ and $$\frac{{d} \overrightarrow{{v}}}{{dt}} \neq 0$$
Subtopic:  Acceleration |
57%
From NCERT
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A particle of mass $$2$$ kg is moving in a circular path with a constant speed of $$10$$ m/s. The change in the magnitude of velocity when a particle travels from $$P$$ to $$Q$$ will be: [assume the radius of the circle is $$10/\pi^2]$$

 1 $$10 \sqrt{3}$$ 2 $$20 \sqrt{3}$$ 3 $$10$$ 4 $$0$$
Subtopic:  Circular Motion |
From NCERT
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To the captain of a ship $$A$$ travelling with velocity $$\overrightarrow{v_{A}} = \left( 3 \hat{i} - 4 \hat{j} \right)$$ km/h, a second ship $$B$$ appears to have a velocity $$\overrightarrow{v_{B}} = \left(5 \hat{i} +12 \hat{j} \right)$$ km/h. What is the true velocity of the ship $$B$$?
1. $$2 \hat{i} + 16 \hat{j}$$ km/h
2. $$13 \hat{i} + 8 \hat{j}$$ km/h
3. $$- 2 \hat{i} - 16 \hat{j}$$ km/h
4. none of these

Subtopic:  Relative Motion |
51%
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An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at $$x=-2~\text{m}$$, its velocity is $$-(4~\text{m/s})\hat j.$$$\stackrel{}{}$ What is the object's acceleration when it is at $$y= 2~\text{m}$$?
1. $$- 8~\text{m/s}^{2} \hat j$$
2. $$- 8~\text{m/s}^{2} \hat i$$
3. $$- 4~\text{m/s}^{2} \hat j$$
4. $$- 4~\text{m/s}^{2} \hat i$$

Subtopic:  Circular Motion |
53%
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The position of a moving particle at time $$t$$ is $$\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$$ Its displacement during the time interval $$t=1$$ s to $$t=3$$ s will be:

 1 $$\hat{j}-\hat{k}$$ 2 $$3\hat{i}-4\hat{j}-\hat{k}$$ 3 $$9\hat{i}+36\hat{j}-27\hat{k}$$ 4 $$32\hat{j}-26\hat{k}$$
Subtopic:  Position & Displacement |
80%
From NCERT
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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

Subtopic:  Position & Displacement |
75%
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Balls $$A$$ and $$B$$ are thrown from two points lying on the same horizontal plane separated by a distance of $$120$$ m. Which of the following statements is correct?

 1 The balls can never meet. 2 The balls can meet if the ball $$B$$ is thrown $$1$$ s later. 3 The two balls meet at a height of $$45$$ m. 4 None of the above
Subtopic:  Relative Motion |
60%
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A body is projected at an angle of $$30^{\circ}$$ with the horizontal with a speed of $$30$$ m/s. What is the angle made by the velocity vector with the horizontal after $$1.5$$ sec? $$\left(g=10~\text{m/s}^2\right)$$
1. $$0^{\circ}$$
2. $$30^{\circ}$$
3. $$60^{\circ}$$
4. $$90^{\circ}$$

Subtopic:  Projectile Motion |
64%
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A particle moves along the positive branch of the curve $$y= \frac{x^{2}}{2}$$ where $$x= \frac{t^{2}}{2}$$, & $$x$$ and $$y$$ are measured in metres and in seconds respectively. At $$t= 2~\text{s}$$, the velocity of the particle will be:
1. $$\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}$$
2. $$\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}$$
3. $$\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}$$
4. $$\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}$$

Subtopic:  Speed & Velocity |
73%
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