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The displacement \(x\) of a particle moving in one dimension under the action of a constant force is related to time t by the equation $t$ $=$ $\sqrt{x}$ $+$ $3$, where \(x\) is in metres and \(t\) is in seconds. What is the displacement of the particle from *t* = 0 s to *t* = 6 s?

1. \(0\)

2. \(12\) m

3. \(6\) m

4. \(18\) m

Subtopic: Distance & Displacement |

58%

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The acceleration \(a\) (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time \(t\) (in \(\mathrm{s}\)) as per the equation \(a=3t+4.\) The velocity of the body at time \(t=2\) \(\mathrm{s}\) will be:

1. \(10~\text{ms}^{-1}\)

2. \(18~\text{ms}^{-1}\)

3. \(14~\text{ms}^{-1}\)

4. \(26~\text{ms}^{-1}\)

Subtopic: Non Uniform Acceleration |

71%

From NCERT

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A point moves in a straight line under the retardation \(av^2\)${\mathrm{}}^{}$. If the initial velocity is \(u,\) the distance covered in \(t\) seconds is:

1. \((aut)\)

2. \(\frac{1}{a}\mathrm{ln}(aut)\)

3. \(\frac{1}{a}\mathrm{ln}(1+aut)\)

4. \(a~\mathrm{ln}(aut)\)

Subtopic: Non Uniform Acceleration |

56%

From NCERT

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The relation between time and distance is given by $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation, as calculated based on this equation, will be (assume *v* to be velocity):

1. $2\alpha {v}^{3}$

2. $2\beta {v}^{3}$

3. $2\alpha \beta {v}^{3}$

4. $2{\beta}^{2}{v}^{3}$

Subtopic: Instantaneous Speed & Instantaneous Velocity |

52%

From NCERT

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The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:

1. | \(b, -4d\) | 2. | \(-b,2c\) |

3. | \(b, ~2c\) | 4. | \(2c, -2d\) |

Subtopic: Non Uniform Acceleration |

81%

From NCERT

PMT - 1999

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An elevator car, whose floor to ceiling distance is equal to \(2.7~\text{m}\), starts ascending with constant acceleration of \(1.2~\text{ms}^{-2}\). \(2\) sec* *after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:

1. \(\sqrt{0.54}~\text{s}\)

2. \(\sqrt{6}~\text{s}\)

3. \(0.7~\text{s}\)

4. \(1~\text{s}\)

Subtopic: Relative Motion in One Dimension |

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The acceleration \(a\) in m/s^{2} of a particle is given by $a=3{t}^{2}+2t+2$ where *t* is the time. If the particle starts out with a velocity, \(u=2\)* *m/s* *at* t = 0*, then the velocity at the end of \(2\) seconds will be:

1. \(12\) m/s

2. \(18\) m/s

3. \(27\) m/s

4. \(36\) m/s

Subtopic: Acceleration |

72%

From NCERT

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A particle moves along a straight line such that its displacement at any time \(t\) is given by \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is:

1. | \(4\) ms^{-1} |
2. | \(-12\) ms^{−1} |

3. | \(42\) ms^{−1} |
4. | \(-9\) ms^{−1} |

Subtopic: Acceleration |

81%

From NCERT

PMT - 1994

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The position \(x\)* *of a particle varies with time *\(t\)* as \(x=at^2-bt^3\). The acceleration of the particle will be zero at time \(t\)* *equal to:

1. | \(\dfrac{a}{b}\) | 2. | \(\dfrac{2a}{3b}\) |

3. | \(\dfrac{a}{3b}\) | 4. | zero |

Subtopic: Acceleration |

84%

From NCERT

PMT - 1997

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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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