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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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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 |

60%

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A particle is moving along the x-axis such that its velocity varies with time as per the equation $\mathrm{v}=20\left(1-\frac{\mathrm{t}}{2}\right)$. 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 |

57%

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Suppose you are riding a bike with a speed of 20 m/s due east relative to a person A who is walking on the ground towards the east. If your friend B walking on the ground due west measures your speed as 30 m/s due east, find the relative velocity between two reference frames A and B:-

1. The velocity of A with respect to B is 5 m/s towards the east

2. The velocity of A with respect to B is 5 m/s towards the west

3. The velocity of A with respect to B is 10 m/s towards the east

4. The velocity of A with respect to B is 10 m/s towards the west

Subtopic: Relative Motion in One Dimension |

63%

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An elevator whose floor to ceiling height is 12 meters, moves upward with an acceleration of $2.2$ $\mathrm{m}/{\mathrm{s}}^{2}$. After 1.5 seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is

1. 1 s

2. 2 s

3. $\sqrt{2}$ s

4. $\sqrt{3}$ s

Subtopic: Relative Motion in One Dimension |

64%

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The position (x) of a particle in a straight line motion is given by $\mathrm{x}=2+10\mathrm{t}-5{\mathrm{t}}^{2}$ $\left(\mathrm{m}\right)$. Its velocity (v) is best represented by?

1. | 2. | ||

3. | 4. |

Subtopic: Graphs |

75%

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A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers 3 consecutive equal distances from the beginning in time ${\mathrm{t}}_{1},$ ${\mathrm{t}}_{2},\mathrm{and}$ ${\mathrm{t}}_{3}$ seconds. The ratio of ${\mathrm{t}}_{1}:{\mathrm{t}}_{2}:{\mathrm{t}}_{3}$ is:

1. 1: 2 : 3

2. $1:\sqrt{2}:\sqrt{3}$

3. $1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2})$

4. $\sqrt{3}:\sqrt{2}:1$

Subtopic: Uniformly Accelerated Motion |

78%

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A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^{2})$

1. | \(340\) m | 2. | \(320\) m |

3. | \(300\) m | 4. | \(360\) m |

Subtopic: Uniformly Accelerated Motion |

82%

From NCERT

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A particle starts from rest (with constant acceleration) and acquires velocity 20 m/s in 5s. The distance travelled by the particle in the next 2 s will be:

1. | 50 m | 2. | 48 m |

3. | 100 m | 4. | 150 m |

Subtopic: Uniformly Accelerated Motion |

72%

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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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