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For a particle, displacement time relation is given by; $t$ $=$ $\sqrt{x}$ $+$ $3$ . 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 |

81%

From NCERT

AIPMT - 1999

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A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards the earth, their respective kinetic energies will be in the ratio of:

1. 1: 4

2. 1: 2

3. 1: $\sqrt{2}$

4. $\sqrt{2}$ :1

Subtopic: Uniformly Accelerated Motion |

83%

From NCERT

AIPMT - 2004

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A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:

where time-average velocity and space-average velocity, respectively, are defined as follows:

$<v{>}_{time}$ $=$ $\frac{\int vdt}{\int dt}$

$<v{>}_{space}$ $=$ $\frac{\int vds}{\int ds}$

1. | \(\frac{1}{2}\) | 2. | \(\frac{3}{4}\) |

3. | \(\frac{4}{3}\) | 4. | \(\frac{3}{2}\) |

Subtopic: Average Speed & Average Velocity |

From NCERT

AIPMT - 1999

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A particle is thrown vertically upward. Its velocity at half its height is \(10\) m/s. Then the maximum height attained by it is: (Assume, \(g=\) \(10\) m/s^{2})

1. \(8\) m

2. \(20\) m

3. \(10\) m

4. \(16\) m

Subtopic: Uniformly Accelerated Motion |

75%

From NCERT

AIPMT - 2001

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If a ball is thrown vertically upwards with speed \(u\), the distance covered during the last \(t\) seconds of its ascent is:

1. \(ut\)

2. \(\frac{1}{2}gt^2\)

3. \(ut-\frac{1}{2}gt^2\)

4. \((u+gt)t\)

Subtopic: Uniformly Accelerated Motion |

65%

From NCERT

AIPMT - 2003

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A man throws some balls with the same speed vertically upwards one after the other at an interval of \(2\) seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given \(g = 9.8\) m/s^{2})

1. | \(19.6\) m/s | More than

2. | \(9.8\) m/s | At least

3. | \(19.6\) m/s | Any speed less than

4. | \(19.6\) m/s | Only with a speed of

Subtopic: Uniformly Accelerated Motion |

67%

From NCERT

AIPMT - 2003

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A body starts falling from height \(h\) and if it travels a distance of \(\frac{h}{2}\) during the last second of motion, then the time of flight is (in seconds):

1. \(\sqrt{2}-1\)

2. \(2+\sqrt{2}\)

3. \(\sqrt{2}+\sqrt{3}\)

4. \(\sqrt{3}+2\)

Subtopic: Uniformly Accelerated Motion |

From NCERT

AIPMT - 1999

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A car is moving with velocity v. It stops after applying breaks at a distance of 20 m. If the velocity of the car is doubled, then how much distance it will cover (travel) after applying breaks?

1. 40 m

2. 80 m

3. 160 m

4. 320 m

Subtopic: Uniformly Accelerated Motion |

81%

From NCERT

AIPMT - 1998

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The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)$\mathrm{}$, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

1. | \(\alpha\) and \(\beta.\) | be independent of

2. | go on increasing with time. |

3. | \(\alpha=\beta.\) | drop to zero when

4. | go on decreasing with time. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

53%

From NCERT

AIPMT - 2005

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The motion of a particle is given by the equation \(S = \left(3 t^{3} + 7 t^{2} + 14 t + 8 \right) \text{m} ,\) The value of the acceleration of the particle at \(t=1~\text{s}\) is:

1. | \(10\) m/s^{2 } |
2. | \(32\) m/s^{2} |

3. | \(23\) m/s^{2} |
4. | \(16\) m/s^{2} |

Subtopic: Acceleration |

93%

From NCERT

AIPMT - 2000

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