A particle is moving along the \(x\text-\)axis with its position \((x)\) varying with time \((t)\) as \(x=\alpha t^{4}+\beta t^{2}+\gamma t+\delta.\) The ratio of its initial velocity to its initial acceleration is:

1. \(2\alpha:\delta \)

2. \(\gamma:2\delta \)

3. \(4\alpha:\beta \)

4. \(\gamma:2\beta \)

1. \(2\alpha:\delta \)

2. \(\gamma:2\delta \)

3. \(4\alpha:\beta \)

4. \(\gamma:2\beta \)

Subtopic: Â Instantaneous Speed & Instantaneous Velocity |

Â 80%

From NCERT

NEET - 2024

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Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by; \(x_p(t)= at+bt^2\) and \(x_Q(t) = ft-t^2. \) At what time do the cars have the same velocity?

1. \(\frac{a-f}{1+b}\)

2. \(\frac{a+f}{2(b-1)}\)

3. \(\frac{a+f}{2(b+1)}\)

4. \(\frac{f-a}{2(1+b)}\)

Subtopic: Â Instantaneous Speed & Instantaneous Velocity |

Â 81%

From NCERT

NEET - 2016

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If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:

1. | \(3A+7B\) | 2. | \(\frac{3}{2}A+\frac{7}{3}B\) |

3. | \(\frac{A}{2}+\frac{B}{3}\) | 4. | \(\frac{3A}{2}+4B\) |

Subtopic: Â Instantaneous Speed & Instantaneous Velocity |

Â 88%

From NCERT

NEET - 2016

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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. | \(24~\text m\) | 2. | \(40~\text m\) |

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

Subtopic: Â Instantaneous Speed & Instantaneous Velocity |

From NCERT

AIPMT - 2006

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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: Â Instantaneous Speed & Instantaneous Velocity |

Â 53%

From NCERT

AIPMT - 2005

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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: Â Instantaneous Speed & Instantaneous Velocity |

Â 82%

From NCERT

AIPMT - 1999

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