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A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are ($\sqrt{3}$, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:

1. \(30^\circ\)

2. \(45^\circ\)

3. \(60^\circ\)

4. \(0\)

Subtopic: Position & Displacement |

76%

From NCERT

AIPMT - 2007

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A car turns at a constant speed on a circular track of radius \(100\) m, taking \(62.8\) s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

1. | \(0,~0\) | 2. | \(0,~10\) m/s |

3. | \(10\) m/s, \(10\) m/s | 4. | \(10\) m/s, \(0\) |

Subtopic: Speed & Velocity |

82%

From NCERT

AIPMT - 2006

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A body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) m/s towards the north. The average acceleration of the body is:

1. \( 7~\text{m/s}^2\)

2. \( \sqrt{7}~\text{m/s}^2\)

3. \(5~\text{m/s}^2\)

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

Subtopic: Acceleration |

77%

From NCERT

AIPMT - 2011

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A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

1. | \(25\) m/s^{2} |
2. | \(36\) m/s^{2} |

3. | \(5\) m/s^{2} |
4. | \(15\) m/s^{2} |

Subtopic: Circular Motion |

80%

From NCERT

AIPMT - 2011

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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)

2. \(\theta = \tan^{-1}(4)\)

3. \(\theta = \tan^{-1}(2)\)

4. \(\theta = 45^{\circ}\)

1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)

2. \(\theta = \tan^{-1}(4)\)

3. \(\theta = \tan^{-1}(2)\)

4. \(\theta = 45^{\circ}\)

Subtopic: Projectile Motion |

75%

From NCERT

AIPMT - 2012

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The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:

1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |

3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |

Subtopic: Projectile Motion |

83%

From NCERT

AIPMT - 2013

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If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?

1. \(90^\circ\)

2. \(45^\circ\)

3. \(180^\circ\)

4. \(0^\circ\)

1. \(90^\circ\)

2. \(45^\circ\)

3. \(180^\circ\)

4. \(0^\circ\)

Subtopic: Resultant of Vectors |

82%

From NCERT

NEET - 2016

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A particle moves in space such that:

\(x=2t^3+3t+4;~y=t^2+4t-1;~z=2\sin\pi t\)

where \(x,~y,~z\) are measured in meters and \(t\) in seconds. The acceleration of the particle at \(t=3\) seconds will be:

1. | \(36 \hat{i}+2 \hat{j}+\hat{k} \) ms^{-2} |

2. | \(36 \hat{i}+2 \hat{j}+\pi \hat{k} \) ms^{-2} |

3. | \(36 \hat{i}+2 \hat{j} \) ms^{-2} |

4. | \(12 \hat{i}+2 \hat{j} \) ms^{-2} |

Subtopic: Acceleration |

68%

From NCERT

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A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\) \((6\) m, \(7\) m) at time \(t=2\) s and \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:

1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |

3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |

Subtopic: Speed & Velocity |

82%

From NCERT

NEET - 2014

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A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)$\stackrel{}{\mathrm{}}$) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:

1. \(5\) m

2. \(10\) m

3. \(15\) m

4. \(20\) m

Subtopic: Uniformly Accelerated Motion |

65%

From NCERT

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