A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x)=βx-2n where, β 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. -2nβ2x-2n-1

2. -2nβ2x-4n-1

3. -2β2x-2n+1

4. 2nβ2e-4n+1

Subtopic:  Acceleration |
 63%
From NCERT
NEET - 2015
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A stone falls under gravity. It covers distances h1, hand h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2, and h3 is

1. h1=2h2=3h3

2. h1=h2/3=h3/5

3. h2=3h1 and h3=3h2

4. h1=h2=h3

Subtopic:  Uniformly Accelerated Motion |
 76%
From NCERT
NEET - 2013
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The motion of a particle along a straight line is described by the equation; \(x=8+12 t-t^3,\) where \(x\) is in metre and \(t\) is in second. The retardation of the particle when its velocity becomes zero is:

1. \(24 ~\text{ms}^{-2} \) 2. zero
3. \( 6 ~\text{ms}^{-2} \) 4. \(12 ~\text{ms}^{-2} \)
Subtopic:  Non Uniform Acceleration |
 74%
From NCERT
NEET - 2012
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A boy standing at the top of a tower of \(20\) m height drops a stone. Assuming \(g=10\) m/s2, the velocity with which it hits the ground will be:
1. \(20\) m/s                                         
2. \(40\) m/s
3. \(5\) m/s                                           
4. \(10\) m/s

Subtopic:  Uniformly Accelerated Motion |
 90%
From NCERT
NEET - 2011
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A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is 

(1) v1v2v1+v2                                         

(2) 2v1v2v1+v2

(3) 2v12v22v12+v22                                         

(4)  v1+v22

Subtopic:  Average Speed & Average Velocity |
 87%
From NCERT
NEET - 2011
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A ball is dropped from a high rise platform at t=0 starting from rest. After 6s another ball is thrown downwards from the same platform with a speed v. The two balls meet at t=18 s. What is the value of v? (take g=10 ms-2)

1. 75 ms-1                                   2. 55 ms-1

3. 40 ms-1                                   4. 60 ms-1

Subtopic:  Relative Motion in One Dimension |
 62%
From NCERT
NEET - 2010
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A particle moves a distance x in time t according to equation x=t+5-1The acceleration of the particle is proportional to, 

1. velocity3/2                                         
2. distance2
3. distance-2                                         
4. velocity2/3

Subtopic:  Acceleration |
 64%
From NCERT
NEET - 2010
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A bus is moving with a speed of \(10~\text{ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100~\text{s}\). If the bus is at a distance of \(1~\text{km}\) from the scooterist, with what minimum speed should the scooterist chase the bus?
1. \(20~\text{ms}^{-1}\)
2. \(40~\text{ms}^{-1}\)
3. \(25~\text{ms}^{-1}\)
4. \(10~\text{ms}^{-1}\)

Subtopic:  Relative Motion in One Dimension |
 75%
From NCERT
NEET - 2009
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The distance travelled by a particle starting from rest and moving with an acceleration 43ms-2, in the third second is 

(1) 6m                             

(2) 4m

(3) 103m                         

(4) 193m

Subtopic:  Uniformly Accelerated Motion |
 77%
From NCERT
NEET - 2008
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A particle shows a 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 |
 70%
From NCERT
NEET - 2008
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