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 |
 68%
From NCERT
NEET - 2015
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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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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 |
 58%
From NCERT
AIPMT - 2010
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A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms-1 to \(20\) ms-1 while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:

1. \(10\) 2. \(1.8\)
3. \(12\) 4. \(9\)
Subtopic:  Uniformly Accelerated Motion |
 78%
From NCERT
AIPMT - 2008
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A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:

1. \(\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}\) 2. \(\sqrt{v_{u} v_{d}}\)
3. \(\frac{v_{d} v_{u}}{v_{d} + v_{u}}\) 4. \(\frac{v_{u} + v_{d}}{2}\)
Subtopic:  Average Speed & Average Velocity |
 82%
From NCERT
AIPMT - 2007
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A particle moves along a straight line OX. At a time \(t\) (in seconds), the displacement \(x\) (in metres) of the particle from O is given by \(x= 40 +12t-t^3\). How long would the particle travel before coming to rest?

1. \(24\) m 2. \(40\) m
3. \(56\) m 4. \(16\) m
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
From NCERT
AIPMT - 2006
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A ball is dropped vertically from a height \(h\) above the ground. It hits the ground and bounces up vertically to a height of \(\frac{h}{2}\). Neglecting subsequent motion and air resistance, its velocity \(v\) varies with the height \(h\) as:
[Take vertically upwards direction as positive.]

1. 2.
3. 4.
Subtopic:  Graphs |
 51%
From NCERT
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The graph of displacement time is given below.

 

Its corresponding velocity-time graph will be:

1. 2.
3. 4.
Subtopic:  Graphs |
 68%
From NCERT
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If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:

1. \(3A+7B\) 2. \(\frac{3}{2}A+\frac{7}{3}B\)
3. \(\frac{A}{2}+\frac{B}{3}\) 4. \(\frac{3A}{2}+4B\)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
From NCERT
NEET - 2016
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A particle moves along a straight line and its position as a function of time is given by \(x= t^3-3t^2+3t+3\) then particle:

1. stops at \(t=1~\text{s}\) and reverses its direction of motion.
2. stops at \(t= 1~\text{s}\) and continues further without a change of direction.
3. stops at \(t=2~\text{s}\) and reverses its direction of motion.
4. stops at \(t=2~\text{s}\) and continues further without a change of direction.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 51%
From NCERT
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