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A particle moving along the x-axis has acceleration \(f,\) at time \(t,\) given by, \(f=f_0\left ( 1-\frac{t}{T} \right ),\) where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0,\) the particle’s velocity \( \left ( v_x \right )\) is:

1. \(f_0T\)

2. \(\frac{1}{2}f_0T^{2}\)

3. \(f_0T^2\)

4. \(\frac{1}{2}f_0T\)

Subtopic: Non Uniform Acceleration |

57%

From NCERT

AIPMT - 2007

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A particle moves along a straight line OX. At a time \(t\) (in seconds), the displacement \(x\) (in metres) of the particle from O is given by \(x= 40 +12t-t^3\). How long would the particle travel before coming to rest?

1. | \(24\) m | 2. | \(40\) m |

3. | \(56\) m | 4. | \(16\) m |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

From NCERT

AIPMT - 2006

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Two bodies, \(A\) (of mass \(1~\text{kg}\)) and \(B\) (of mass \(3~\text{kg}\)) are dropped from heights of \(16~\text{m}\) and \(25~\text{m}\), respectively. The ratio of the time taken by them to reach the ground is:

1. \(\frac{5}{4}\)

2. \(\frac{12}{5}\)

3. \(\frac{5}{12}\)

4. \(\frac{4}{5}\)

Subtopic: Uniformly Accelerated Motion |

80%

From NCERT

AIPMT - 2006

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A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:

1. | \(\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}\) | 2. | \(\sqrt{v_{u} v_{d}}\) |

3. | \(\frac{v_{d} v_{u}}{v_{d} + v_{u}}\) | 4. | \(\frac{v_{u} + v_{d}}{2}\) |

Subtopic: Average Speed & Average Velocity |

82%

From NCERT

AIPMT - 2007

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The position of a particle with respect to time \(t\) along the \(\mathrm{x}\)-axis is given by \(9t^{2}-t^{3}\) where x is in metre and \(t\) in second. What will be the position of this particle when it achieves maximum speed along the \(+\mathrm{x}\) direction?

1. \(32\) m

2. \(54\) m

3. \(81\) m

4. \(24\) m

Subtopic: Non Uniform Acceleration |

77%

From NCERT

AIPMT - 2007

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A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms^{-1} to \(20\) ms^{-1} while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:

1. | \(10\) | 2. | \(1.8\) |

3. | \(12\) | 4. | \(9\) |

Subtopic: Uniformly Accelerated Motion |

79%

From NCERT

AIPMT - 2008

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A particle shows the 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 |

79%

From NCERT

AIPMT - 2008

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The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms^{-2}, in the third second is:

1. \(6\) m

2. \(4\) m

3. \(\frac{10}{3}\) m

4. \(\frac{19}{3}\) m

Subtopic: Distance & Displacement |

79%

From NCERT

AIPMT - 2008

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A particle starts its motion from rest under the action of a constant force. If the distance covered in the first \(10\) s is \(S_1\) and that covered in the first \(20\) s is \(S_2\), then:

1. \(S_2=2S_1\)

2. \(S_2 = 3S_1\)

3. \(S_2 = 4S_1\)

4. \(S_2= S_1\)

Subtopic: Acceleration |

70%

From NCERT

AIPMT - 2009

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A bus is moving at a speed of \(10\) ms^{-1} on a straight road. A scooterist wishes to overtake the bus in \(100\) s. If the bus is at a distance of \(1\) km from the scooterist, with what speed should the scooterist chase the bus?

1. \(20\) ms^{-1}

2. \(40\) ms^{-1}

3. \(25\) ms^{-1}

4. \(10\) ms^{-1}

2. \(40\) ms

3. \(25\) ms

4. \(10\) ms

Subtopic: Relative Motion in One Dimension |

77%

From NCERT

AIPMT - 2009

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