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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 car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:

1. | \(60\) km | 2. | \(30 \sqrt{2}\) km |

3. | \(30 \sqrt{5}\) km | 4. | \(60 \sqrt{2}\) km |

Subtopic: Distance & Displacement |

70%

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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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For the given acceleration \(\left ( a \right )\) versus time \(\left ( t \right )\) graph of a body, the body is initially at rest.

From the following, the velocity \(\left ( v \right )\) versus time \(\left ( t \right )\) graph will be:

1. | 2. | ||

3. | 4. |

Subtopic: Non Uniform Acceleration |

62%

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The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)$\mathrm{}$, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

1. | \(\alpha\) and \(\beta.\) | be independent of

2. | go on increasing with time. |

3. | \(\alpha=\beta.\) | drop to zero when

4. | go on decreasing with time. |

Subtopic: Instantaneous Speed & Instantaneous Velocity |

52%

From NCERT

AIPMT - 2005

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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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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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When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity \({v_0}\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Expression for stopping distance of a vehicle in terms of \({v_0}\) and \(a\) is:

1. | \(\dfrac{{v_o}^2}{2a}\) | 2. | \(\dfrac{{v_o}}{2a}\) |

3. | \(\dfrac{{v_o}^2}{a}\) | 4. | \(\dfrac{2a}{{v_o}^2}\) |

Subtopic: Acceleration |

83%

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The position of an object moving along the x-axis is given by, \(x=a+bt^2\), where \(a=8.5 \) m, \(b=2.5\) ms^{–2}, and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:

1. \(13\) m/s

2. \(17\) m/s

3. \(10\) m/s

4. \(0\)

Subtopic: Instantaneous Speed & Instantaneous Velocity |

85%

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The figure shows the displacement-time graph of a particle moving on the x-axis. Then,

1. | the particle is continuously going in a positive x-direction. |

2. | the particle is at rest. |

3. | the velocity increases up to a time \(t_0\), and then becomes constant. |

4. | the particle moves at a constant velocity up to a time \(t_0\), and then stops. |

Subtopic: Graphs |

69%

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