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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $\mathrm{v}\left(\mathrm{x}\right)$ $={\mathrm{\beta x}}^{-2\mathrm{n}}$ where $\mathrm{\beta}$ and \(\mathrm{n}\) are constants and \(\mathrm{x}\) is the position of the particle. The acceleration of the particle as a function of \(\mathrm{x}\) is given by:

1. $-2{\mathrm{n\beta}}^{2}{\mathrm{x}}^{-2\mathrm{n}-1}$

2. $-2{\mathrm{n\beta}}^{2}{\mathrm{x}}^{-4\mathrm{n}-1}$

3. $-2{\mathrm{\beta}}^{2}{\mathrm{x}}^{-2\mathrm{n}+1}$

4. $-2{\mathrm{n\beta}}^{2}{\mathrm{x}}^{-4\mathrm{n}+1}$

Subtopic: Non Uniform Acceleration |

68%

From NCERT

NEET - 2015

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A particle is moving such that its position coordinates (x, y) are (\(2\) m, \(3\) m) at time \(t=0,\) (\(6\) m,\(7\) m) at time \(t=2\) s, and (\(13\) m, \(14\) m) at time \(t=\) \(5\) s. The average velocity vector \(\vec{v}_{avg}\) from \(t=\) 0 to \(t=\) \(5\) s is:

1. \({1 \over 5} (13 \hat{i} + 14 \hat{j})\)

2. \({7 \over 3} (\hat{i} + \hat{j})\)

3. \(2 (\hat{i} + \hat{j})\)

4. \({11 \over 5} (\hat{i} + \hat{j})\)

Subtopic: Average Speed & Average Velocity |

76%

From NCERT

AIPMT - 2014

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A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:

1. | \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |

2. | \(h_2=3h_1\) and \(h_3=3h_2\) |

3. | \(h_1=h_2=h_3\) |

4. | \(h_1=2h_2=3h_3\) |

Subtopic: Uniformly Accelerated Motion |

82%

From NCERT

AIPMT - 2013

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The displacement \(x\) (in m) of a particle of mass \(m\) (in kg) moving in one dimension under the action of a force, is related to time \(t\) (in s) by, \(t = \sqrt x +3 \). The displacement of the particle when its velocity is zero will be:

1. \(4\) m

2. zero

3. \(6\) m

4. \(2\) m

1. \(4\) m

2. zero

3. \(6\) m

4. \(2\) m

Subtopic: Instantaneous Speed & Instantaneous Velocity |

90%

From NCERT

NEET - 2013

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A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after \(10\) s will be:

1. \(9 \sqrt{2}~ \text{units}\)2. \(5 \sqrt{2} ~\text{ units}\)

3. \(5~\text{units}\)

4. \(9~\text{units}\)

Subtopic: Uniformly Accelerated Motion |

87%

From NCERT

AIPMT - 2012

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The motion of a particle along a straight line is described by the equation \(x = 8+12t-t^3\) where \(x \) is in meter and \(t\) in seconds. The retardation of the particle, when its velocity becomes zero, is:

1. \(24\) ms^{-2}

2. zero

3. \(6\) ms^{-2}

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

Subtopic: Acceleration |

75%

From NCERT

AIPMT - 2012

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A boy standing at the top of a tower of 20 m height drops a stone. Assuming \(g=\) 10 ms^{-2}, the velocity with which it hits the ground is:

1. | 20 m/s | 2. | 40 m/s |

3. | 5 m/s | 4. | 10 m/s |

Subtopic: Uniformly Accelerated Motion |

91%

From NCERT

AIPMT - 2011

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A particle covers half of its total distance with speed ν_{1} and the rest half distance with speed ν_{2}.

Its average speed during the complete journey is:

1. $\frac{{v}_{1}+{v}_{2}}{2}$

2. $\frac{{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$

3. $\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$

4. $\frac{{v}_{1}^{2}{v}_{2}^{2}}{{v}_{1}^{2}+{v}_{2}^{2}}$

Subtopic: Average Speed & Average Velocity |

89%

From NCERT

AIPMT - 2011

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A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds, another ball is thrown downwards from the same platform with speed v. The two balls meet after 18 seconds. What is the value of v?

1. | 75 ms^{-1} |
2. | 55 ms^{-1} |

3. | 40 ms^{-1} |
4. | 60 ms^{-2} |

Subtopic: Uniformly Accelerated Motion |

58%

From NCERT

AIPMT - 2010

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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. (velocity)^{\(3/2\)}

2. (distance)^{\(2\)}

3. (distance)^{\(-2\)}

4. (velocity)^{\(2/3\)}

Subtopic: Acceleration |

70%

From NCERT

AIPMT - 2010

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