The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:

1. | \(0.4\) s | 2. | \(0.25\) s |

3. | \(0.5\) s | 4. | \(0.3\) s |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

87%

From NCERT

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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: Instantaneous Speed & Instantaneous Velocity |

88%

From NCERT

NEET - 2016

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The position of an object moving along the x-axis is given by, \(x=a+bt^2\) where \(a=8.5\) m, \(b=2.5\) ms^{-2}, and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:

1. \(13\) m/s

2. \(17\) m/s

3. \(10\) m/s

4. \(0\)

Subtopic: Instantaneous Speed & Instantaneous Velocity |

86%

From NCERT

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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. \(0\)

4. none of the above

Subtopic: Instantaneous Speed & Instantaneous Velocity |

81%

From NCERT

AIPMT - 1999

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The position x of a particle moving along the x-axis varies with time t as x = $20\mathrm{t}$ $-$ $5{\mathrm{t}}^{2}$, where x is in meters and t is in seconds. The particle reverses its direction of motion at:

1. x = 40 m

2. x = 10 m

3. x = 20 m

4. x = 30 m

Subtopic: Instantaneous Speed & Instantaneous Velocity |

80%

From NCERT

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The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is:

1. | \(24\) metres | 2. | \(12\) metres |

3. | \(5\) metres | 4. | zero |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

76%

From NCERT

PMT - 2000

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A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:

1. | zero velocity. | 2. | zero acceleration. |

3. | non-zero velocity. | 4. | non-zero acceleration. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

72%

From NCERT

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Which of the following four statements is false?

1. | A body can have zero velocity and still be accelerated. |

2. | A body can have a constant velocity and still have a varying speed. |

3. | A body can have a constant speed and still have a varying velocity. |

4. | The direction of the velocity of a body can change when its acceleration is constant. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

65%

From NCERT

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A particle moves along a straight line and its position as a function of time is given by$\mathrm{}$ \(x= t^3-3t^2+3t+3\)

1. | \(t=1~\text{s}\) and reverses its direction of motion | stops at

2. | \(t= 1~\text{s}\) and continues further without a change of direction | stops at

3. | \(t=2~\text{s}\) and reverses its direction of motion | stops at

4. | \(t=2~\text{s}\) and continues further without a change of direction | stops at

Subtopic: Instantaneous Speed & Instantaneous Velocity |

51%

From NCERT

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The relation between time and distance is given by $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation, as calculated based on this equation, will be (assume *v* to be velocity) :

1. $2\alpha {v}^{3}$

2. $2\beta {v}^{3}$

3. $2\alpha \beta {v}^{3}$

4. $2{\beta}^{2}{v}^{3}$

Subtopic: Instantaneous Speed & Instantaneous Velocity |

52%

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