A particle has an initial velocity (\(2\hat{i}+3\hat{j}\)) and an acceleration (\(0.3\hat{i}+0.2\hat{j}\)). The magnitude of velocity after \(10\) s will be:

1. \(9 \sqrt{2} ~\text{units} \)

2. \(5 \sqrt{2} ~\text{units} \)

3. \(5 ~\text{units} \)

4. \(9~\text{units} \)

Subtopic: Â Uniformly Accelerated Motion |

Â 88%

From NCERT

NEET - 2012

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A particle has an initial velocity \(\overrightarrow{u} = \left(4 \hat{i} - 5 \hat{j}\right)\) m/s and it is moving with an acceleration \(\overrightarrow{a} = \left(\frac{1}{4} \hat{i} + \frac{1}{5} \hat{j}\right)\text{m/s}^{2}\). Velocity of the particle at \(t=2\) s will be:

1. \((6\hat i -4\hat j)~\text{m/s}\)

2. \((4.5\hat i -4.5\hat j)~\text{m/s}\)

3. \((4.5\hat i -4.6\hat j)~\text{m/s}\)

4. \((6\hat i -4.6\hat j)~\text{m/s}\)

Subtopic: Â Uniformly Accelerated Motion |

Â 86%

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A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s^{2} along the north. The velocity of the body just after \(4\) s will be?

1. | \(8\) m/s along East. |

2. | \(4 \sqrt{2} \) m/s along North-East. |

3. | \(8\) m/s along North. |

4. | \(4 \sqrt{2} \) m/s along South-East. |

Subtopic: Â Uniformly Accelerated Motion |

Â 78%

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A body sliding on a smooth inclined plane requires \(4\) seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top?

1. | \(1~\text{s}\) | 2. | \(2~\text{s}\) |

3. | \(4~\text{s}\) | 4. | \(16~\text{s}\) |

Subtopic: Â Uniformly Accelerated Motion |

Â 70%

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The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane \(9.8~\text{m}\) long (angle of inclination is $\mathrm{}$\(30^{\circ}\)

** **

1. | \(\frac{1}{2}~\text{sec} \) | 2. | \(2 ~\text{sec} \) |

3. | \(4~ \text{sec} \) | 4. | \(1~\text{sec} \) |

Subtopic: Â Uniformly Accelerated Motion |

Â 70%

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A particle starts from the origin at \(t=0\) sec with a velocity of \(10\hat j~\text{m/s}\) and moves in the \(x\text-y\) plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)~\text{m/s}^2\). At what time is the \(x\text-\)coordinate of the particle \(16\) m?

1. \(2\) s

2. \(3\) s

3. \(4\) s

4. \(1\) s

Subtopic: Â Uniformly Accelerated Motion |

Â 70%

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A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2\). What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84\) m?

1. \(36\) m/s

2. \(26\) m/s

3. \(1\) m/s

4. \(0\) m/s

Subtopic: Â Uniformly Accelerated Motion |

Â 70%

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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: Â Uniformly Accelerated Motion |

Â 65%

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A body is slipping from an inclined plane of height *\(h\)* and length \(l\). If the angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is:

1. \(\sqrt{\frac{2 h}{g}}\)

2. \(\sqrt{\frac{2 l}{g}}\)

3. \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)

4. \(\sin \theta \sqrt{\frac{2 h}{g}}\)

Subtopic: Â Uniformly Accelerated Motion |

Â 59%

From NCERT

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A frictionless wire \(AB\) is fixed on a sphere of radius \(R\). A very small spherical ball slips on this wire. The time taken by this ball to slip from \(A\) to \(B\) is:

1. \(\frac{2 \sqrt{g R}}{g \cos \theta}\)

2. \(2 \sqrt{g R} . \frac{\cos \theta}{g}\)

3. \(2 \sqrt{\frac{R}{g}}\)

4. \(\frac{g R}{\sqrt{g\cos \theta}}\)

Subtopic: Â Uniformly Accelerated Motion |

Â 53%

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