A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to \(v(x)= βx^{- 2 n}\) where \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\) is given by:
1. \(- 2 nβ^{2} x^{- 2 n - 1}\) 2. \(- 2 nβ^{2} x^{- 4 n - 1}\)
3. \(- 2 \beta^{2} x^{- 2 n + 1}\) 4. \(- 2 nβ^{2} x^{- 4 n + 1}\)
Subtopic:  Non Uniform Acceleration |
 69%
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 |
 77%
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 |
 88%
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 |
 76%
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 |
 90%
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-1
Subtopic:  Uniformly Accelerated Motion |
 59%
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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