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A passenger arriving in a new town wishes to go from the station to a hotel located \(10\) km away on a straight road from the station. A dishonest cabman takes him along a circuitous path \(23\) km long and reaches the hotel in \(28\) min. The average speed of the taxi is:

1. \(30\) km/h

2. \(49.3\) km/h

3. \(55.6\) km/h

4. \(60\) km/h

Subtopic: Average Speed & Average Velocity |

75%

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On a long horizontally moving belt (as shown in the figure) a child runs to and fro with a speed $9km{h}^{-1}$ (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of $4km{h}^{-1}$. For an observer on a stationary platform outside, what is the speed of the child running in the direction of motion of the belt?

1. 5 kmh^{-1}

2. \(\sqrt{41}\) kmh^{-1}

3. 21 kmh^{-1}

4. 13 kmh^{-1}

Subtopic: Relative Motion in One Dimension |

59%

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A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to \(49~\text{ms}^{-1}.\) How much time does the ball take to return to his hands?

1. \(5\) s

2. \(10\) s

3. \(15\) s

4. \(7\) s

Subtopic: Uniformly Accelerated Motion |

76%

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The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?

1. | Interval 2 | 2. | Interval 1 |

3. | Interval 3 | 4. | Equal in all intervals |

Subtopic: Acceleration |

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The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) & \(3,\) respectively are:

1. | \(-,-,+\) |

2. | \(+,-,+\) |

3. | \(-,+,+\) |

4. | \(+,+,-\) |

Subtopic: Average Speed & Average Velocity |

89%

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A police van moving on a highway with a speed of $30km{h}^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192km{h}^{-1}$. If the muzzle speed of the bullet is $150m{s}^{-1},$ with what speed does the bullet hit the thief’s car?

$\left(1\right)103m{s}^{-1}$

$\left(2\right)105m{s}^{-1}$

$\left(3\right)101m{s}^{-1}$

$\left(4\right)102m{s}^{-1}$

Subtopic: Relative Motion in One Dimension |

69%

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The instantaneous speed is always:

1. | less than the magnitude of instantaneous velocity. |

2. | greater than the magnitude of instantaneous velocity. |

3. | equal to the magnitude of instantaneous velocity. |

4. | may be less or greater than the magnitude of instantaneous velocity. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

61%

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A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?

1. | \(6\) km/h | 2. | \(5\) km/h |

3. | \(5.6\) km/h | 4. | \(6.6\) km/h |

Subtopic: Average Speed & Average Velocity |

62%

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A particle in one-dimensional motion:

1. | with zero speed at an instant may have non-zero acceleration at that instant. |

2. | with zero speed may have non-zero velocity. |

3. | with constant speed, must have non-zero acceleration. |

4. | with a positive value of acceleration must be speeding up. |

Subtopic: Acceleration |

53%

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A player throws a ball upwards with an initial speed of \(29.4 \text{ ms}^{- 1}\). What is the direction of acceleration during the upward motion of the ball?

1. | vertically downwards |

2. | vertically upwards |

3. | first upwards then downwards |

4. | none of the above |

Subtopic: Uniformly Accelerated Motion |

75%

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