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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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 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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A bus is moving at a speed of \(10\) ms-1 on a straight road. A scooterist wishes to overtake the bus in \(100\) s. If the bus is at a distance of \(1\) km from the scooterist, with what speed should the scooterist chase the bus?
1. \(20\) ms-1
2. \(40\) ms-1
3. \(25\) ms-1
4. \(10\) ms-1
Subtopic:  Relative Motion in One Dimension |
 77%
From NCERT
AIPMT - 2009
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A particle starts its motion from rest under the action of a constant force. If the distance covered in the first \(10\) s is \(S_1\) and that covered in the first \(20\) s is \(S_2\), then:
1. \(S_2=2S_1\)
2. \(S_2 = 3S_1\)
3. \(S_2 = 4S_1\)
4. \(S_2= S_1\)

Subtopic:  Acceleration |
 70%
From NCERT
AIPMT - 2009
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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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