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A ball is bouncing elastically with a speed of \(1\) m/s between the walls of a railway compartment of size \(10\) m in a direction perpendicular to the walls. The train is moving at a constant velocity of \(10\) m/s parallel to the direction of motion of the ball. As seen from the ground:

(a) | the direction of motion of the ball changes every \(10\) sec. |

(b) | the speed of the ball changes every \(10\) sec. |

(c) | the average speed of the ball over any \(20\) sec intervals is fixed. |

(d) | the acceleration of the ball is the same as from the train. |

Choose the correct option:

1. | (a), (c), (d) | 2. | (a), (c) |

3. | (b), (c), (d) | 4. | (a), (b), (c) |

Subtopic: Relative Motion in One Dimension |

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If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0\), then:

1. | the displacement in time \(T\) must always take non-negative values. |

2. | the displacement \(x\) in time \(T\) satisfies \(-{v_0T} \lt x \lt {v_0T}\). |

3. | the acceleration is always a non-negative number. |

4. | the motion has no turning points. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

55%

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A body is thrown upwards and reaches its maximum height. At that position:

1. | its velocity is zero and its acceleration is also zero. |

2. | its velocity is zero but its acceleration is maximum. |

3. | its acceleration is minimum. |

4. | its velocity is zero and its acceleration is the acceleration due to gravity. |

Subtopic: Uniformly Accelerated Motion |

83%

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Which one of the following displacement-time graph represents two moving objects \(P\) and \(Q\) with zero relative velocity?

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

85%

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A body is projected vertically in the upward direction from the surface of the earth. If the upward direction is taken as positive, then the acceleration of the body during its upward and downward journey is:

1. Positive, negative

2. Negative, negative

3. Positive, positive

4. Negative, positive

Subtopic: Acceleration |

63%

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When the velocity of a body is variable, then:

1. | its speed may be constant |

2. | its acceleration may be constant |

3. | its average acceleration may be constant |

4. | all of the above |

Subtopic: Acceleration |

71%

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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%

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If a body travels some distance in a given time interval, then for that time interval, its:

1. | Average speed ≥ |Average velocity| |

2. | |Average velocity| ≥ Average speed |

3. | Average speed < |Average velocity| |

4. | |Average velocity| must be equal to average speed. |

Subtopic: Average Speed & Average Velocity |

84%

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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 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 |

62%

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