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Which one is not an example of a point object?

1. | A railway carriage moving without jerks between two stations. |

2. | A monkey sitting on top of a man cycling smoothly on a circular track. |

3. | A plane under a journey of several thousand kilometres. |

4. | A tumbling beaker that has slipped off the edge of a table. |

Subtopic: Distance & Displacement |

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A drunkard walking in a narrow lane takes \(5\) steps forward and \(3\) steps backward, followed again by \(5\) steps forward and \(3\) steps backward, and so on. Each step is \(1\) m long and requires \(1\) s. There is a pit on the road \(13\) m away from the starting point. The drunkard will fall into the pit after:

1. \(37\) s

2. \(31\) s

3. \(29\) s

4. \(33\) s

Subtopic: Distance & Displacement |

61%

From NCERT

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The speed-time graph of a particle moving along a fixed direction is shown in the figure. Then the distance traversed by the particle between \(t=0\) s to \(10\) s is:

1. \(70\) m

2. \(60\) m

3. \(50\) m

4. \(40\) m

Subtopic: Graphs |

90%

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The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval ${t}_{1}$ to ${t}_{2}$?

1. | \(x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a\left(t_2-t_1\right)^2\) |

2. | \(\mathrm{v}\left(\mathrm{t}_2\right)=\mathrm{v}\left(\mathrm{t}_1\right)+\mathrm{a}\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |

3. | \(x\left(t_2\right)=x\left(t_1\right)+v_{\text {average }}\left(t_2-t_1\right)+\left(\frac{1}{2}\right) a_{\text {average }}\left(t_2-t_1\right)^2\) |

4. | \(\mathrm{v}_{\text {average }}=\left(\mathrm{x}\left(\mathrm{t}_2\right)-\mathrm{x}\left(\mathrm{t}_1\right)\right) /\left(\mathrm{t}_2-\mathrm{t}_1\right)\) |

Subtopic: Average Speed & Average Velocity |

53%

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The figure gives the x-t plot of a particle executing a one-dimensional simple harmonic motion. Then the signs of position & velocity variables of the particle at t = -1.2 sec respectively are:

$\left(1\right)\mathrm{positive},\mathrm{negative}$

$\left(2\right)\mathrm{positive},\mathrm{positive}$

$\left(3\right)\mathrm{negative},\mathrm{positive}$

$\left(4\right)\mathrm{negative},\mathrm{negative}$

Subtopic: Instantaneous Speed & Instantaneous Velocity |

52%

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The position-time \((x-t)\) graphs for two children \(A\) and \(B\) returning from their school O to their homes P and Q respectively are shown in the graph. Choose the incorrect statement.

1. | \(B\) reaches home faster than \(A.\) |

2. | \(B\) overtakes \(A\) on the road twice. |

3. | \(B\) walks faster than \(A.\) |

4. | \(A\) lives closer to the school than \(B.\) |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

60%

From NCERT

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A jet airplane travelling at the speed of $500km{h}^{-1}$ ejects its products of combustion at the speed of $1500km{h}^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

$1.1000km{h}^{-1}$

$2.500km{h}^{-1}$

$3.1500km{h}^{-1}$

$4.2000km{h}^{-1}$

Subtopic: Relative Motion in One Dimension |

55%

From NCERT

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A car moving along a straight highway with a speed of \(126\) km/h is brought to a stop within a distance of \(200\) m. How long does it take for the car to stop?

1. \(10.2\) s

2. \(9.6\) s

3. \(11.4\) s

4. \(6.7\) s

Subtopic: Uniformly Accelerated Motion |

72%

From NCERT

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Two trains A and B of length \(400\) m each are moving on two parallel tracks with a uniform speed of \(72\) km/h in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by \(1\) m/s^{2}. If after \(50\) s, the guard of B just brushes past the driver of A, what was the original distance between them?

1. \(2000\) m

2. \(2250\) m

3. \(1200\) m

4. \(1250\) m

Subtopic: Uniformly Accelerated Motion |

52%

From NCERT

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On a two-lane road, car A is travelling at a speed of \(36\) kmh^{-1}. Two cars B and C approach car A in opposite directions with a speed of \(54\) kmh^{-1} each. At a certain instant, when the distance AB is equal to AC, both being \(1\) km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?

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

2. \(5\) ms^{-2}

3. \(2\) ms^{-2}

4. \(3\) ms^{-2}

Subtopic: Uniformly Accelerated Motion |

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