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A body is moving along a straight line according to the equation of motion, \(x= t^{2} - 3 t + 4\), where \(x\) is in metre and \(t\) is in seconds. What is the acceleration of the body when it comes to rest?

1. zero

2. \(2~\text{m/s}^2\)

3. \(\frac{3}{2}~\text{m/s}^2\)

4. \(1~\text{m/s}^2\)

Subtopic: Acceleration |

84%

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A particle is allowed to fall from rest from a height \(h\). Which of the following represents its velocity versus time graph?

1. | 2. | ||

3. | 4. |

Subtopic: Uniformly Accelerated Motion |

60%

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A particle is moving along the positive \(x\)-axis with some initial velocity. The acceleration-time graphs are shown. In which case the velocity of the particle will increase for the entire time between \(t_1\) and \(t_2\)?

1. | only in (II) |

2. | in (I) and (III) |

3. | in (I) and (II) |

4. | in (I), (II) and (III) |

Subtopic: Graphs |

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The graph below shows position as a function of time for two trains running on parallel tracks.

Which of the following statements is true?

1. | At time \(t_B \) both the trains have the same velocity |

2. | Both the trains have the same velocity at some time after \(t_B \) |

3. | Both the trains have the same velocity at some time before \(t_B \) |

4. | Both the trains have the same acceleration |

Subtopic: Graphs |

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Two stones are thrown vertically up simultaneously with different velocities. Which of the following graphs represents the relative separation \((\Delta y)\) between them as a function of time \((t)\)?

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

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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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Starting from rest, a car accelerates uniformly at the rate of \(1~\text{m/s}^2\) for some time, then decelerates uniformly at the rate of \(2~\text{m/s}^2\) and finally comes to rest after a journey of \(1\) minute. The maximum possible speed of the car during this journey is:

1. \(10\) m/s

2. \(20\) m/s

3. \(30\) m/s

4. \(40\) m/s

Subtopic: Uniformly Accelerated Motion |

62%

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A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right)\). At \(t=0\) particle is at the origin. From the following, select the correct position \((x)\) - time \((t)\) plot for the particle:

1. | 2. | ||

3. | 4. |

Subtopic: Non Uniform Acceleration |

58%

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A helicopter moving vertically upwards releases a packet when it is at a certain height above the ground. The packet initially moves upwards for a time \(t_1\) and then falls downwards for a time \(t_2\) until it reaches the ground. Then:

1. \(t_1<t_2\)

2. \(t_1=t_2\)

3. \(t_1>t_2\)

4. Data insufficient

Subtopic: Uniformly Accelerated Motion |

63%

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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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