A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) =βx-2n where β and \(\mathrm{n}\) are constants and \(\mathrm{x}\) is the position of the particle. The acceleration of the particle as a function of \(\mathrm{x}\) is given by:
1. -22x-2n-1
2. -22x-4n-1
3. -2β2x-2n+1
4. -22x-4n+1

Subtopic:  Non Uniform Acceleration |
 68%
From NCERT
NEET - 2015
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A particle is moving such that its position coordinates (x, y) are (\(2\) m, \(3\) m) at time \(t=0,\) (\(6\) m,\(7\) m) at time \(t=2\) s, and (\(13\) m, \(14\) m) at time \(t=\) \(5\) s. The average velocity vector \(\vec{v}_{avg}\) from \(t=\) 0 to \(t=\) \(5\) s is:
1. \({1 \over 5} (13 \hat{i} + 14 \hat{j})\)
2. \({7 \over 3} (\hat{i} + \hat{j})\)
3. \(2 (\hat{i} + \hat{j})\)
4. \({11 \over 5} (\hat{i} + \hat{j})\)

Subtopic:  Average Speed & Average Velocity |
 76%
From NCERT
AIPMT - 2014
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A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:

1. \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)
2. \(h_2=3h_1\) and \(h_3=3h_2\)
3. \(h_1=h_2=h_3\)
4. \(h_1=2h_2=3h_3\)
Subtopic:  Uniformly Accelerated Motion |
 82%
From NCERT
AIPMT - 2013
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The displacement \(x\) (in m) of a particle of mass \(m\) (in kg) moving in one dimension under the action of a force, is related to time \(t\) (in s) by, \(t = \sqrt x +3 \) . The displacement of the particle when its velocity is zero will be:
1. \(4\) m
2. zero
3. \(6\) m
4. \(2\) m
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 90%
From NCERT
NEET - 2013
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A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after \(10\) s will be:
1. \(9 \sqrt{2}~   \text{units}\)
2. \(5 \sqrt{2}  ~\text{ units}\)
3. \(5~\text{units}\)
4. \(9~\text{units}\)

Subtopic:  Uniformly Accelerated Motion |
 87%
From NCERT
AIPMT - 2012
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The motion of a particle along a straight line is described by the equation \(x = 8+12t-t^3\) where \(x \) is in meter and \(t\) in seconds. The retardation of the particle, when its velocity becomes zero, is:
1. \(24\) ms-2
2. zero
3. \(6\) ms-2
4. \(12\) ms-2

Subtopic:  Acceleration |
 75%
From NCERT
AIPMT - 2012
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A boy standing at the top of a tower of 20 m height drops a stone. Assuming \(g=\) 10 ms-2, the velocity with which it hits the ground is:
1. 20 m/s 2. 40 m/s
3. 5 m/s 4. 10 m/s
Subtopic:  Uniformly Accelerated Motion |
 91%
From NCERT
AIPMT - 2011
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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 |
 88%
From NCERT
AIPMT - 2011
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A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds, another ball is thrown downwards from the same platform with speed v. The two balls meet after 18 seconds. What is the value of v?

1. 75 ms-1 2. 55 ms-1
3. 40 ms-1 4. 60 ms-2
Subtopic:  Uniformly Accelerated Motion |
 58%
From NCERT
AIPMT - 2010
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A particle moves a distance \(x\) in time \(t\) according to equation \(x=(t+5)^{-1}.\) The acceleration of the particle is proportional to:
1. (velocity)\(3/2\)
2. (distance)\(2\)
3. (distance)\(-2\)
4. (velocity)\(2/3\)

Subtopic:  Acceleration |
 70%
From NCERT
AIPMT - 2010
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