# If a ball is thrown vertically upwards with speed $$u$$, the distance covered during the last $$t$$ seconds of its ascent is: 1. $$ut$$ 2. $$\frac{1}{2}gt^2$$ 3. $$ut-\frac{1}{2}gt^2$$ 4. $$(u+gt)t$$

Subtopic:  Uniformly Accelerated Motion |
65%
From NCERT
AIPMT - 2003
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A man throws some balls with the same speed vertically upwards one after the other at an interval of $$2$$ seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given $$g = 9.8$$ m/s2)

 1 More than $$19.6$$ m/s 2 At least $$9.8$$ m/s 3 Any speed less than $$19.6$$ m/s 4 Only with a speed of $$19.6$$ m/s
Subtopic:  Uniformly Accelerated Motion |
66%
From NCERT
AIPMT - 2003
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A particle is thrown vertically upward. Its velocity at half its height is $$10$$ m/s. Then the maximum height attained by it is: (Assume, $$g=$$ $$10$$ m/s2
1. $$8$$ m
2. $$20$$ m
3. $$10$$ m
4. $$16$$ m

Subtopic:  Uniformly Accelerated Motion |
74%
From NCERT
AIPMT - 2001
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A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:
where time-average velocity and space-average velocity, respectively, are defined as follows:

$}_{time}$ $=$ $\frac{\int vdt}{\int dt}$
$}_{space}$ $=$ $\frac{\int vds}{\int ds}$

 1 $$\frac{1}{2}$$ 2 $$\frac{3}{4}$$ 3 $$\frac{4}{3}$$ 4 $$\frac{3}{2}$$
Subtopic:  Average Speed & Average Velocity |
From NCERT
AIPMT - 1999
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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards the earth, their respective kinetic energies will be in the ratio of:

1. 1: 4

2. 1: 2

3. 1: $\sqrt{2}$

4. $\sqrt{2}$ :1

Subtopic:  Uniformly Accelerated Motion |
83%
From NCERT
AIPMT - 2004
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For a particle, displacement time relation is given by; $t$ $=$ $\sqrt{x}$ $+$ $3$ . Its displacement, when its velocity is zero will be:
1. $$2$$ m
2. $$4$$ m
3. $$0$$ m
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
81%
From NCERT
AIPMT - 1999
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A body starts falling from height $$h$$ and if it travels a distance of $$\frac{h}{2}$$ during the last second of motion, then the time of flight is (in seconds):
1. $$\sqrt{2}-1$$
2. $$2+\sqrt{2}$$
3. $$\sqrt{2}+\sqrt{3}$$
4. $$\sqrt{3}+2$$

Subtopic:  Uniformly Accelerated Motion |
From NCERT
AIPMT - 1999
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A small block slides down on a smooth inclined plane starting from rest at time $$t=0.$$ Let $$S_n$$ be the distance traveled by the block in the interval $$t=n-1$$ to $$t=n.$$ Then the ratio $$\dfrac{S_n}{S_{n +1}}$$ is:

 1 $$\dfrac{2n+1}{2n-1}$$ 2 $$\dfrac{2n}{2n-1}$$ 3 $$\dfrac{2n-1}{2n}$$ 4 $$\dfrac{2n-1}{2n+1}$$
Subtopic:  Uniformly Accelerated Motion |
57%
From NCERT
NEET - 2021
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A car is moving with velocity v. It stops after applying breaks at a distance of 20 m. If the velocity of the car is doubled, then how much distance it will cover (travel) after applying breaks?
1.  40 m
2.  80 m
3.  160 m
4.  320 m

Subtopic:  Uniformly Accelerated Motion |
81%
From NCERT
AIPMT - 1998
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The displacement $$x$$ of a particle varies with time $$t$$ as $$x = ae^{-\alpha t}+ be^{\beta t}$$$\mathrm{}$, where $$a,$$ $$b,$$ $$\alpha,$$ and $$\beta$$ are positive constants. The velocity of the particle will:

 1 be independent of $$\alpha$$ and $$\beta.$$ 2 go on increasing with time. 3 drop to zero when $$\alpha=\beta.$$ 4 go on decreasing with time.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
52%
From NCERT
AIPMT - 2005
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