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. v1+v22

2. v1v2v1+v2

3. 2v1v2v1+v2

4. v12v22v12+v22

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 \(x = ae^{-\alpha t}+ be^{\beta t}\), 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 = 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: 2

4. 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: 

<v>time = vdtdt
<v>space = vdsds

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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