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 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. \(0.4~\text s\)  2. \(0.25~\text s\) 
3. \(0.5~\text s\)  4. \(0.3~\text s\) 
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 88%
From NCERT
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The position of an object moving along the \(x\text-\)axis is given by, \(x=a+bt^2\)where \(a=8.5 ~\text m,\)  \(b=2.5~\text{m/s}^2,\) and \(t\) is measured in seconds. Its velocity at \(t=2.0~\text s\) will be:
1. \(13~\text{m/s}\) 
2. \(17~\text{m/s}\)
3. \(10~\text{m/s}\)
4. \(0~\text{m/s}\)

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 87%
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. \(0\) m
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 82%
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 |
 82%
From NCERT
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The position of an object moving along the \(\mathrm x\)-axis is given by \(x = a+bt^{2}\) where \(a=10\) m, \(b=2\) ms-2 and \(t\) is in seconds. The velocity at \(t=3.0\) s is:
1. \(12\) ms-1
2. \(20\) ms-1
3. \(36\) ms-1
4. \(46\) ms-1
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 85%
From NCERT
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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 |
 74%
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 |
 68%
From NCERT
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The position-time \((x\text-t)\) graphs for two children \(A\) and \(B\) returning from their school \(O\) to their homes \(P\) and \(Q\) respectively are shown in the graph. 
         
 
Choose the incorrect statement:

1. \(B\) reaches home faster than \(A.\)
2. \(B\) overtakes \(A\) on the road twice.
3. \(B\) walks faster than \(A.\)
4. \(A\) lives closer to the school than \(B.\)
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 62%
From NCERT
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If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0,\) then:

1. the displacement in time \(T\) must always take non-negative values.
2. the displacement \(x\) in time \(T\) satisfies  \(-{v_0T} \lt x \lt {v_0T}.\)
3. the acceleration is always a non-negative number.
4. the motion has no turning points.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 56%
From NCERT
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