# Two particles move from $$A$$ to $$C$$ and $$A$$ to $$D$$ on a circle of radius $$R$$ and diameter $$AB$$. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:                                  1. $$2$$ 2. $$2\sqrt{3}$$ 3. $$\sqrt{3}$$ 4. $$\dfrac{\sqrt{3}}{2}$$

Subtopic:  Speed & Velocity |
63%
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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.
Subtopic:  Acceleration |
69%
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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.
Subtopic:  Acceleration |
72%
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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

Subtopic:  Relative Motion |
88%
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A man can row a boat with a speed of $$10$$ kmph in still water. The river flows at $$6$$ kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width $$1$$ km is:
1. $$\frac{1}{8}~\text{h}$$
2. $$\frac{1}{4}~\text{h}$$
3. $$\frac{1}{2}~\text{h}$$
4. $$1~\text{h}$$

Subtopic:  Relative Motion |
72%
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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 $$30$$ kmph towards $$W$$ 2 $$30$$ kmph towards $$S\text-W$$ 3 $$42.4$$ kmph towards $$S\text-W$$ 4 $$42.4$$ kmph towards $$N\text-W$$
Subtopic:  Speed & Velocity |
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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
Subtopic:  Projectile Motion |
76%
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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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A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:

 1 $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2 $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3 $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4 $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 
Subtopic:  Position & Displacement |
75%
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The position vector of a particle is $$\vec{r}= a \sin\omega t \hat{i} + a\cos \omega t \hat{j}$$. The velocity of the particle is:
 1 parallel to the position vector. 2 at $$60^{\circ}$$ with position vector. 3 parallel to the acceleration vector. 4 perpendicular to the position vector.
Subtopic:  Circular Motion |
80%
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