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 |
 66%
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Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind car \(B\), the driver of the car \(A\) applied the brake producing uniform retardation \(a\). There will be no collision when:
1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)
2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)
3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)
4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

Subtopic:  Relative Motion in One Dimension |
 59%
From NCERT
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Assertion (A): Displacement of a body may be zero when distance travelled by it is not zero.
Reason (R): The displacement is the longest distance between initial and final position.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.
Subtopic:  Distance & Displacement |
 85%
From NCERT
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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. \((\text{velocity})^{\frac{3}{2}}\) 2. \((\text{distance})^2\)
3. \((\text{distance})^{-2}\) 4. \((\text{velocity})^{\frac{2}{3}}\)
Subtopic:  Acceleration |
 66%
From NCERT
NEET - 2010
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A particle shows 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 |
 73%
From NCERT
NEET - 2008
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A particle moves in a straight line, according to the law \(x=4a[t+a\sin(t/a)], \) where \(x\) is its position in metres, \(t\) is in seconds & \(a\) is some constant, then the velocity is zero at:

1. \(x = 4 a^2\pi\) metres 2. \(t = \pi\) sec
3. \(t =0\) sec 4. none of the above
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 \(x^2= t^2+1\). Its acceleration in \(\text{m/s}^2\) at time \(1\) sec is:
1. \(\frac{1}{x}\)
2. \(\frac{1}{x} - \frac{1}{x^{3}}\)
3. \(\frac{2}{x}\)
4. \(-\frac{t^2}{x^3}\)

Subtopic:  Acceleration |
 50%
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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 |
 81%
From NCERT
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The initial velocity of a particle is \(u\) (at \(t=0\)) and the acceleration \(f\) is given by \(at\). Which of the following relation is valid?
1. \(v = u + a t^{2}\)
2. \(v = u + a \frac{t^{2}}{2}\)
3. \(v = u + a t\)
4. \(v= u\)

Subtopic:  Non Uniform Acceleration |
From NCERT
PMT - 1981
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A stone falls freely from rest from a height \(h\) and it travels a distance of \(\frac{9 h}{25}\) in the last second. The value of \(h\) is:

1. \(145\) m 2. \(100\) m
3. \(122.5\) m 4. \(200\) ms
Subtopic:  Uniformly Accelerated Motion |
 71%
From NCERT
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