The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:

1. \(0.4\) s 2. \(0.25\) s
3. \(0.5\) s 4. \(0.3\) s
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 87%
From NCERT
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If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:

1. \(3A+7B\) 2. \(\frac{3}{2}A+\frac{7}{3}B\)
3. \(\frac{A}{2}+\frac{B}{3}\) 4. \(\frac{3A}{2}+4B\)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
From NCERT
NEET - 2016
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The position of an object moving along the x-axis is given by, \(x=a+bt^2\)  where \(a=8.5\) m,
\(b=2.5\) ms-2
and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:
1. \(13\) m/s
2. \(17\) m/s
3. \(10\) m/s
4. \(0\) 

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 86%
From NCERT
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For a particle, displacement time relation is given by t = x + 3 . Its displacement, when its velocity is zero will be:
1. \(2\) m
2. \(4\) m
3. \(0\)
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 81%
From NCERT
AIPMT - 1999
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The position \(x\) of a particle moving along the \(x\)-axis varies with time \(t\) as \(x=20t-5t^2,\)
where \(x\) is in meters and \(t\) is in seconds. The particle reverses its direction of motion at:

1. \(x=40~\text{m}\)
2. \(x=10~\text{m}\)
3. \(x=20~\text{m}\)
4. \(x=30~\text{m}\)

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 80%
From NCERT
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The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is: 

1. \(24\) metres 2. \(12\) metres
3. \(5\) metres 4. zero
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 76%
From NCERT
PMT - 2000
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A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:

1. zero velocity. 2. zero acceleration.
3. non-zero velocity. 4. non-zero acceleration.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 72%
From NCERT
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Which of the following four statements is false?

1. A body can have zero velocity and still be accelerated.
2. A body can have a constant velocity and still have a varying speed.
3. A body can have a constant speed and still have a varying velocity.
4. The direction of the velocity of a body can change when its acceleration is constant.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 65%
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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The relation between time and distance is given by t=αx2+βx, where α and β are constants. The retardation, as calculated based on this equation, will be (assume v to be velocity):
1. 2αv3
2. 2βv3
3. 2αβv3
4. 2β2v3

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 52%
From NCERT
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