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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%

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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 |

66%

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Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2\) \((v_1>v_2).\) When the car \(A\) is at a distance \(d\) behind car \(B\), the driver of the car \(A\) applied the brake producing uniform retardation \(a\)*.* There will be no collision when:

1. \(d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}\)

2. \(d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

3. \(d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}\)

4. \(d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}\)

Subtopic: Relative Motion in One Dimension |

59%

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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. | \((\text{velocity})^{\frac{3}{2}}\) | 2. | \((\text{distance})^2\) |

3. | \((\text{distance})^{-2}\) | 4. | \((\text{velocity})^{\frac{2}{3}}\) |

Subtopic: Acceleration |

66%

From NCERT

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The position \(x\) of a particle moving along the \(x\)-axis varies with time \(t\) as \(x=20t-5t^2,\)

where \(x\) is in meters and \(t\) is in seconds. The particle reverses its direction of motion at:

1. \(x=40~\text{m}\)

2. \(x=10~\text{m}\)

3. \(x=20~\text{m}\)

4. \(x=30~\text{m}\)

Subtopic: Instantaneous Speed & Instantaneous Velocity |

81%

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A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers \(3\) consecutive equal distances from the beginning in time \(t_1, t_2,\text{and}~t_3\)${\mathrm{}}_{}$ seconds. The ratio of \(t_1:t_2:t_3\) is:

1. \(1:2:3\)

2. \(1:\sqrt{2}:\sqrt{3}\)

3. \(1:\left(\sqrt{2}-1\right):\left(\sqrt{3}-\sqrt{2}\right)\)

4. \(\sqrt{3}:\sqrt{2}:1\)$\mathrm{}$

Subtopic: Uniformly Accelerated Motion |

79%

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The position (\(x\)) of a particle in a straight line motion is given by \(x = 2 + 10 t - 5 t^{2}~\text{m}\). Its velocity (\(v\)) is best represented by?

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

76%

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An elevator whose floor to ceiling height is \(12\) meters, moves upward with an acceleration of \(2.2~\text{m/s}^2\). After \(1.5\) seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is:

1. \(1~\text{s}\)

2. \(2~\text{s}\)

3. \(\sqrt{2}~\text{s}\)

4. \(\sqrt{3}~\text{s}\)

Subtopic: Relative Motion in One Dimension |

64%

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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%

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The velocity \(v\) of an object varies with its position \(x\) on a straight line as \(v=3\sqrt{x}.\) Its acceleration versus time \((a\text-t)\) graph is best represented by:

1. | 2. | ||

3. | 4. |

Subtopic: Acceleration |

61%

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