A person travelling in a straight line moves with a constant velocity \(v_1\) for a certain distance \(x\) and with a constant velocity \(v_2\) for the next equal distance. The average velocity \(v\) is given by the relation:

1. \(\frac{1}{v} = \frac{1}{v_1}+\frac{1}{v_2}\) 2. \(\frac{2}{v} = \frac{1}{v_1}+\frac{1}{v_2}\)
3. \(\frac{v}{2} = \frac{v_1+v_2}{2}\) 4. \(v = \sqrt{v_1v_2}\)

Subtopic:  Average Speed & Average Velocity |
 77%
From NCERT
NEET - 2019
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A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time t1 if the elevator is moving uniformly and time t2 if the elevator is stationary. Then:

1. \(t_1<t_2 \) or \(t_1>t_2 \) depending upon whether the lift is going up or down.
2. \(t_1<t_2 \)
3. \(t_1>t_2 \)
4. \(t_1=t_2 \)

Subtopic:  Relative Motion in One Dimension |
 52%
From NCERT
NEET - 2019
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Two bodies, \(A\) (of mass \(1~\text{kg}\)) and \(B\) (of mass \(3~\text{kg}\)) are dropped from heights of \(16~\text{m}\) and \(25~\text{m}\), respectively. The ratio of the time taken by them to reach the ground is:
1. \(\frac{5}{4}\)
2. \(\frac{12}{5}\)
3. \(\frac{5}{12}\)
4. \(\frac{4}{5}\)

Subtopic:  Uniformly Accelerated Motion |
 80%
From NCERT
AIPMT - 2006
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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 particle moving along the x-axis has acceleration \(f,\) at time \(t,\) given by, \(f=f_0\left ( 1-\frac{t}{T} \right ),\)  where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0,\) the particle’s velocity \( \left ( v_x \right )\) is:
1. \(f_0T\)
2. \(\frac{1}{2}f_0T^{2}\)
3. \(f_0T^2\)
4. \(\frac{1}{2}f_0T\)

Subtopic:  Non Uniform Acceleration |
 57%
From NCERT
AIPMT - 2007
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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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The position of a particle with respect to time \(t\) along the \(\mathrm{x}\)-axis is given by \(9t^{2}-t^{3}\) where x is in metre and \(t\) in second. What will be the position of this particle when it achieves maximum speed along the \(+\mathrm{x}\) direction?
1. \(32\) m
2. \(54\) m
3. \(81\) m
4. \(24\) m

Subtopic:  Non Uniform Acceleration |
 77%
From NCERT
AIPMT - 2007
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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 particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

         

1. B
2. C
3. D
4. A

Subtopic:  Graphs |
 79%
From NCERT
AIPMT - 2008
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The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms-2, in the third second is:
1. \(6\) m
2. \(4\) m
3. \(\frac{10}{3}\) m
4. \(\frac{19}{3}\) m

Subtopic:  Distance & Displacement |
 79%
From NCERT
AIPMT - 2008
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