# A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of $$1~\text{m}$$ each will then be: 1.  All equal, being equal to $$\sqrt{2 / g}$$ s.  2. In the ratio of the square roots of the integers $$1,2,3....$$ 3.  In the ratio of the difference in the square roots of the integers $$\sqrt{1}$$, $$(\sqrt{2}-\sqrt{1})$$,$$(\sqrt{3}-\sqrt{2})$$,$$(\sqrt{4}-\sqrt{3})$$ $$\ldots$$  4.  In the ratio of the reciprocal of the square roots of the integers i.e,... $$\frac{1}{\sqrt{1}}$$, $$\frac{1}{\sqrt{2}}$$, $$\frac{1}{\sqrt{3}}$$,$$\frac{1}{\sqrt{4}}$$

Subtopic:  Uniformly Accelerated Motion |
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The graph between the displacement $$x$$ and time $$t$$ for a particle moving in a straight line is shown in the figure.

During the interval OA, AB, BC and CD the acceleration of the particle is:

 OA AB BC CD 1. + 0 + + 2. – 0 + 0 3. + 0 – + 4. – 0 – 0
Subtopic:  Graphs |
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PMT - 1986
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A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers?

 1 $$3.6~\text{m}$$ 2 $$28.8~\text{m}$$ 3 $$36.0~\text{m}$$ 4 It cannot be calculated from the above graph.
Subtopic:  Graphs |
68%
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The velocity-time $$(v\text-t)$$ graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $$6$$ s are, respectively:

1. $$8$$ m, $$16$$ m
2. $$16$$ m, $$8$$ m
3. $$16$$ m, $$16$$ m
4. $$8$$ m, $$8$$ m

Subtopic:  Graphs |
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In the following graph, the distance travelled by the body in metres is:

 1 $$200$$ 2 $$250$$ 3 $$300$$ 4 $$400$$
Subtopic:  Graphs |
86%
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Which graph represents a uniformly accelerated motion?

 1 2 3 4
Subtopic:  Graphs |
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Which of the following velocity-time graphs shows a realistic situation for a body in motion?

 1 2 3 4

Subtopic:  Graphs |
87%
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AIIMS - 2004
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Acceleration-time graph of a body is shown.

The corresponding velocity-time graph of the same body is:

 1 2 3 4
Subtopic:  Graphs |
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PMT - 2004
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Given below are two statements:

 Assertion (A): Position-time graph of a stationary object is a straight line parallel to the time axis. Reason (R): For a stationary object, the position does not change with time.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Distance & Displacement |
88%
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The acceleration of a particle starting from rest varies with time according to the relation $$A= - a\omega^2\sin \omega t$$. The displacement of this particle at a time $$t$$ will be:

 1 $$-\frac{1}{2}\left(a\omega^2\sin\omega t\right)t^2$$ 2 $$a\omega \sin \omega t$$ 3 $$a\omega \cos \omega t$$ 4 $$a\sin \omega t$$
Subtopic:  Non Uniform Acceleration |
60%
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