# A particle covers half of its total distance with speed ν1 and the rest half distance with speed ν2. Its average speed during the complete journey is: 1. $\frac{{v}_{1}+{v}_{2}}{2}$ 2. $\frac{{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$ 3. $\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$ 4. $\frac{{v}_{1}^{2}{v}_{2}^{2}}{{v}_{1}^{2}+{v}_{2}^{2}}$

Subtopic:  Average Speed & Average Velocity |
89%
From NCERT
AIPMT - 2011
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The motion of a particle is given by the equation $$S = \left(3 t^{3} + 7 t^{2} + 14 t + 8 \right) \text{m} ,$$ The value of the acceleration of the particle at $$t=1~\text{s}$$ 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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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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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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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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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 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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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 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. $$\frac{1}{2}gt^2$$
3. $$ut-\frac{1}{2}gt^2$$
4. $$(u+gt)t$$

Subtopic:  Uniformly Accelerated Motion |
65%
From NCERT
AIPMT - 2003
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