The coordinate of an object is given as a function of time by x=7t-3t2, where x is in metres and t is in seconds. Its average velocity over the interval t=0 to t=4 is will be:

1.  5 m/s

2.  -5 m/s

3.  11 m/s

4.  -11 m/s

Subtopic:  Average Speed & Average Velocity |
 72%
From NCERT
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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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A particle moves in a straight line, according to the law x=4at+a sinta , where x is its position in meters, t is in sec & a is some constant, then the velocity is zero at :

(1)  x=4a2π meters

(2)  t=π sec

(3)  t=0 sec

(4)  none

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
From NCERT
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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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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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