A point moves in a straight line so that its displacement is x m at time t sec, given by x2=t2+1. Its acceleration in m/s2 at time 1 sec is:

(1)  1x

(2)  1x-1x3

(3)  1x3

(4)  -t2x3

Subtopic:  Non Uniform Acceleration |
 56%
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If the velocity of a particle is \(\mathrm{v}=\mathrm{At}+\mathrm{Bt^{2}},\) where \(\mathrm{A}\) and \(\mathrm{B}\) are constants, then the distance travelled by it between \(1\) s and \(2\) s is:
1. \(3\mathrm{A}+7\mathrm{B}\)
2. \(\frac{3}{2}\mathrm{A}+\frac{7}{3}\mathrm{B}\)
3. \(\frac{\mathrm{A}}{2}+\frac{\mathrm{B}}{3}\)
4. \(\frac{\mathrm{3A}}{2}+\mathrm{4B}\)

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
From NCERT
NEET - 2016
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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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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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NEET 2023 - Target Batch - Aryan Raj Singh

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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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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