# The angle turned by a body undergoing circular motion depends on the time as given by the equation, $$\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}$$. It can be deduced that the angular acceleration of the body is?  1. $$\theta_1$$ 2. $$\theta_2$$ 3. $$2\theta_1$$ 4. $$2\theta_2$$

Subtopic:  Circular Motion |
84%
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A particle is moving eastwards with velocity of $$5$$ m/s. In $$10$$ seconds the velocity changes to $$5$$ m/s northwards. The average acceleration in this time is?

 1 zero 2 $$\frac{1}{\sqrt{2}}~ \text{m/s}^2$$ toward north-west 3 $$\frac{1}{\sqrt{2}}~\text{m/s}^2$$ toward north-east 4 $$\frac{1}{2}~\text{m/s}^2$$ toward north-west
Subtopic:  Acceleration |
64%
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A vector $\stackrel{\to }{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $|\Delta \stackrel{\to }{a}|$ and $\Delta a$ are, respectively:

 1 $$0, ad\theta$$ 2 $$a d\theta, 0$$ 3 $$0,0$$ 4 None of these
Subtopic:  Position & Displacement |
53%
From NCERT
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A particle is moving such that its position coordinates $$(x,y)$$ are $$(2$$ m, $$3$$ m) at time $$t=0,$$ $$(6$$ m, $$7$$ m) at time $$t=2$$ s and $$(13$$ m, $$14$$ m) at time $$t=5$$ s. Average velocity vector $$(v_{avg})$$ from $$t=0$$ to $$t=5$$ s is:

 1 $$\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )$$ 2 $$\frac{7}{3}\left ( \hat{i}+\hat{j} \right )$$ 3 $$2\left ( \hat{i}+\hat{j} \right )$$ 4 $$\frac{11}{5}\left ( \hat{i}+\hat{j} \right )$$
Subtopic:  Speed & Velocity |
82%
From NCERT
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The coordinates of a moving particle at a time $$t$$, are given by, $$x= 5\sin 10t, y = 5\cos 10t$$. It can be deduced that the speed of the particle will be:

 1 $$25$$ units 2 $$50$$ units 3 $$10$$ units 4 $$30$$ units
Subtopic:  Speed & Velocity |
54%
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What determines the nature of the path followed by a particle:
1. Speed
2. Velocity
3. Acceleration
4. Both (2) and (3)

Subtopic:  Projectile Motion |
77%
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A swimmer swims a distance d upstream in $$4$$ s and swims an equal distance downstream in $$2$$ s. The ratio of swimmer's speed in still water to the speed of river water will be:

 1 $$\frac{6}{5}$$ 2 $$\frac{3}{1}$$ 3 $$\frac{5}{3}$$ 4 $$\frac{4}{3}$$
Subtopic:  Relative Motion |
76%
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In $$1.0~\text{s}$$, a particle goes from point $$A$$ to point $$B$$, moving in a semicircle of radius $$1.0~\text{m}$$ (see figure). The magnitude of the average velocity is:

 1 $$3.14~\text{m/s}$$ 2 $$2.0~\text{m/s}$$ 3 $$1.0~\text{m/s}$$ 4 zero
Subtopic:  Speed & Velocity |
77%
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Certain neutron stars are believed to be rotating at about $$1$$ rev/s. If such a star has a radius of $$20$$ km, the acceleration of an object on the equator of the star will be:

 1 $$20 \times 10^8 ~\text{m/s}^2$$ 2 $$8 \times 10^5 ~\text{m/s}^2$$ 3 $$120 \times 10^5 ~\text{m/s}^2$$ 4 $$4 \times 10^8 ~\text{m/s}^2$$
Subtopic:  Circular Motion |
70%
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A river is flowing from $$W$$ to $$E$$ with a speed of $$5$$ m/min. A man can swim in still water with a velocity of $$10$$ m/min. In which direction should the man swim so as to take the shortest possible path to go to the south:

 1 $$30^{\circ}$$ with downstream 2 $$60^{\circ}$$ with downstream 3 $$120^{\circ}$$ with downstream 4 South
Subtopic:  Relative Motion |
60%
From NCERT
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