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 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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The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3\). The speed of the particle at time \(t\) is given by:

1. | \(\sqrt{\alpha^{2} + \beta^{2}}\) | 2. | \(3t \sqrt{\alpha^{2} + \beta^{2}}\) |

3. | \(3t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) | 4. | \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) |

Subtopic: Speed & Velocity |

79%

From NCERT

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Two particles \(A\) and \(B\), move with constant velocities \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\). At the initial moment their position vector are \(\overrightarrow {r_1}\) and \(\overrightarrow {r_2}\) respectively. The condition for particles \(A\) and \(B\) for their collision to happen will be:

1. | \(\overrightarrow{r_{1 }} . \overrightarrow{v_{1}} = \overrightarrow{r_{2 }} . \overrightarrow{v_{2}}\) | 2. | \(\overrightarrow{r_{1}} \times\overrightarrow{v_{1}} = \overrightarrow{r_{2}} \times \overrightarrow {v_{2}}\) |

3. | \(\overrightarrow{r_{1}}-\overrightarrow{r_{2}}=\overrightarrow{v_{1}} - \overrightarrow{v_{2}}\) | 4. | \(\frac{\overrightarrow{r_{1}} - \overrightarrow{r_{2}}}{\left|\overrightarrow{r_{1}} - \overrightarrow{r_{2}}\right|} = \frac{\overrightarrow{v_{2}} - \overrightarrow{v_{1}}}{\left|\overrightarrow{v_{2}} - \overrightarrow{v_{1}}\right|}\) |

Subtopic: Speed & Velocity |

71%

From NCERT

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Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and diameter \(AB\). If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:

1. \(2\)

2. \(2\sqrt{3}\)

3. \(\sqrt{3}\)

4. \(\dfrac{\sqrt{3}}{2}\)

Subtopic: Speed & Velocity |

63%

From NCERT

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The position of a particle is given by;

\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in metres. The magnitude and direction of \(\vec{v}(t)\) at\(t=1.0\) s are:

1. \(4\)m/s,\(53^\circ\) with \(x\)-axis

2. \(4\) m/s, \(37^\circ\) with \(x\)-axis

3. \(5\) m/s,\(53^\circ\) with \(y\)-axis

4. \(5\)m/s, \(53^\circ\) with \(x\)-axis

\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in metres. The magnitude and direction of \(\vec{v}(t)\) at\(t=1.0\) s are:

1. \(4\)m/s,\(53^\circ\) with \(x\)-axis

2. \(4\) m/s, \(37^\circ\) with \(x\)-axis

3. \(5\) m/s,\(53^\circ\) with \(y\)-axis

4. \(5\)m/s, \(53^\circ\) with \(x\)-axis

Subtopic: Speed & Velocity |

68%

From NCERT

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A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:

1. | \(30\) kmph towards \(W\) |

2. | \(30\) kmph towards \(S\text-W\) |

3. | \(42.4\) kmph towards \(S\text-W\) |

4. | \(42.4\) kmph towards \(N\text-W\) |

Subtopic: Speed & Velocity |

58%

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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