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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 vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $\left|\Delta \overrightarrow{a}\right|$ and $\Delta a$ are, respectively:

1. | \(0, ad\theta\) | 2. | \(a d\theta, 0\) |

3. | \(0,0\) | 4. | None of these |

Subtopic: Position & Displacement |

53%

From NCERT

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The angle turned by a body undergoing circular motion depends on the time as given by the equation, \(\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}\). It can be deduced that the angular acceleration of the body is?

1. \(\theta_1\)

2. \(\theta_2\)

3. \(2\theta_1\)

4. \(2\theta_2\)

Subtopic: Circular Motion |

84%

From NCERT

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Certain neutron stars are believed to be rotating at about \(1\) rev/s. If such a star has a radius of \(20\) km, the acceleration of an object on the equator of the star will be:

1. | \(20 \times 10^8 ~\text{m/s}^2\) | 2. | \(8 \times 10^5 ~\text{m/s}^2\) |

3. | \(120 \times 10^5 ~\text{m/s}^2\) | 4. | \(4 \times 10^8 ~\text{m/s}^2\) |

Subtopic: Circular Motion |

70%

From NCERT

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Three particles are moving with constant velocities \(v_1 ,v_2\) and \(v\) respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among \(v_1 ,v_2\) and \(v\) is:

1. \(v =v_1+v_2\)

2. \(v= \sqrt{v_{1} v_{2}}\)

3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)

4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)

Subtopic: Speed & Velocity |

53%

From NCERT

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A body is projected with velocity \(\vec{v} = \left( \alpha \hat{i} + \beta \hat{j} \right)~\text{m/s}\). The time of flight of the body is: [considering \(x\) as horizontal and \(y\) as vertical axis and \(g\) is acceleration due to gravity]

1. \(\frac{2 \beta}{g}\)

2. \(\frac{2 \alpha}{g}\)

3. \(\frac{2 \alpha \beta}{g}\)

4. \(\frac{2 \alpha}{g \beta}\)

1. \(\frac{2 \beta}{g}\)

2. \(\frac{2 \alpha}{g}\)

3. \(\frac{2 \alpha \beta}{g}\)

4. \(\frac{2 \alpha}{g \beta}\)

Subtopic: Projectile Motion |

77%

From NCERT

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A car moves on a circular path such that its speed is given by \(v= Kt\), where \(K\) = constant and \(t\) is time. Also given: radius of the circular path is \(r\). The net acceleration of the car at time \(t\) will be:

1. \(\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}\)

2. \(2K\)

3. \(K\)

4. \(\sqrt{K^{2} + K^{2} t^{2}}\)

Subtopic: Circular Motion |

80%

From NCERT

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Raindrops are falling with speed \(v\) vertically downwards and a man is running on a horizontal road with speed \(u.\) The magnitude of the velocity of the raindrops with respect to the man is:

1. \(v-u\)

2. \(v+u\)

3. \(\sqrt{{v}^2 + {u}^2 \over 2}\)

4. \(\sqrt{{v}^2 + {u}^2}\)

Subtopic: Relative Motion |

82%

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The equation of trajectory of a projectile is given by \(y = x-10x^{2}\). Its speed of projection is: (\(g =1 0\) m/${\mathrm{s}}^{2}$)

1. \(1\) m/s

2. \(2\) m/s

3. \(3\) m/s

4. \(4\) m/s

Subtopic: Projectile Motion |

73%

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A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:

1. \(t=6\) s

2. \(t=7\) s

3. \(t=8\) s

4. \(t=14\) s

Subtopic: Projectile Motion |

75%

From NCERT

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