# 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. 1/2 2. 3/4 3. 4/3 4. 3/2

Subtopic:  Average Speed & Average Velocity |
From NCERT
AIPMT - 1999
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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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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. $\frac{1}{2}{\mathrm{gt}}^{2}$

3. $\mathrm{ut}-\frac{1}{2}{\mathrm{gt}}^{2}$

4. $\left(\mathrm{u}+\mathrm{gt}\right)\mathrm{t}$

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 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. $$0$$
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 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 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 |
80%
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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The motion of a particle is given by the equation $S=\left(3{t}^{3}+7{t}^{2}+14t+8\right)m,$ The value of the acceleration of the particle at t = 1 s is :

 1 10 m/s2 2 32 m/s2 3 23 m/s2 4 16 m/s2
Subtopic:  Acceleration |
93%
From NCERT
AIPMT - 2000
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