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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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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 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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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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The graph of displacement time is given below.

Its corresponding velocity-time graph will be:

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

69%

From NCERT

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

1. \(- 2 nβ^{2} x^{- 2 n - 1}\)

2. \(- 2 nβ^{2} x^{- 4 n - 1}\)

3. \(- 2 \beta^{2} x^{- 2 n + 1}\)

4. \(- 2 nβ^{2} x^{- 4 n + 1}\)

${\mathrm{}}^{}$

Subtopic: Non Uniform Acceleration |

68%

From NCERT

NEET - 2015

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A particle moves along a path \(ABCD\) as shown in the figure. The magnitude of the displacement of the particle from \(A\) to \(D\) is:

1. $(5+10\sqrt{2})$m

2. \(10\) m

3. $15\sqrt{2}$ m

4. \(15\) m

Subtopic: Distance & Displacement |

70%

From NCERT

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Acceleration-time graph of a body is shown.

** **

The corresponding velocity-time graph of the same body is:

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

65%

From NCERT

PMT - 2004

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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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For the given acceleration \(\left ( a \right )\) versus time \(\left ( t \right )\) graph of a body, the body is initially at rest.

From the following, the velocity \(\left ( v \right )\) versus time \(\left ( t \right )\) graph will be:

1. | 2. | ||

3. | 4. |

Subtopic: Non Uniform Acceleration |

62%

From NCERT

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