# 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 |
74%
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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 |
59%
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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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A deer wants to save her life from a lion. The lion follows a path whose equation is $$x^{2} + y^{2} = 16$$. For saving her life, the deer needs to move on a path whose equation will be:
1. $$x^{2} + y^{2} = 4$$
2. $$x^{2} + y^{2} = 16$$
3. $$x^{2} + y^{2} - 64 = 0$$
4. Both (1) and (3) are correct.​​​​​​​

Subtopic:  Circular Motion |
64%
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A particle rotates in a circular path starting from rest. If angular acceleration is $$4~\text{rad/s}^{2}$$, then the time after which angle between net acceleration and tangential acceleration becomes $$45^{\circ}$$ is?

 1 $$0.5$$ s 2 $$0.25$$ s 3 $$2$$ s 4 $$4$$ s
Subtopic:  Circular Motion |
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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%
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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 |
52%
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A particle has an initial velocity $$\overrightarrow{u} = \left(4 \hat{i} - 5 \hat{j}\right)$$ m/s and it is moving with an acceleration $$\overrightarrow{a} = \left(\frac{1}{4} \hat{i} + \frac{1}{5} \hat{j}\right)\text{m/s}^{2}$$. Velocity of the particle at $$t=2$$ s will be:
1. $$(6\hat i -4\hat j)~\text{m/s}$$
2. $$(4.5\hat i -4.5\hat j)~\text{m/s}$$
3. $$(4.5\hat i -4.6\hat j)~\text{m/s}$$
4. $$(6\hat i -4.6\hat j)~\text{m/s}$$

Subtopic:  Uniformly Accelerated Motion |
86%
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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 |
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