The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:

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

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

3. \(4~\text{m/s}^2\)

4. zero

Subtopic: Â Acceleration |

Â 87%

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The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:

1. | \(5\hat{i}~\text{m/s}^2\) | 2. | \(-4\hat{i}~\text{m/s}^2\) |

3. | \(-8\hat{j}~\text{m/s}^2\) | 4. | \(0\) |

Subtopic: Â Acceleration |

Â 82%

From NCERT

NEET - 2017

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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: Â Acceleration |

Â 76%

From NCERT

AIPMT - 2011

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If the position of a particle varies according to the equations \(x= 3t^2\)${\mathrm{}}^{}$, \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?

1. | Velocities in \(y\) and \(z\) directions are constant |

2. | Acceleration in the \(x\text-\)direction is non-uniform |

3. | Acceleration in the \(x\text-\)direction is uniform |

4. | Motion is not in a straight line |

Subtopic: Â Acceleration |

Â 75%

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A particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:

1. | Acceleration is zero at \(t=1\) sec. |

2. | Speed is zero at \(t=0\) sec. |

3. | Acceleration is always zero. |

4. | Speed is \(3\) m/s at \(t=1\) sec. |

Subtopic: Â Acceleration |

Â 71%

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A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?

1. | Velocity and acceleration, both are parallel to \(r\). |

2. | Velocity is perpendicular to \(r\) and acceleration is directed towards the origin. |

3. | Velocity is not perpendicular to \(r\) and acceleration is directed away from the origin. |

4. | Velocity and acceleration, both are perpendicular to \(r\). |

Subtopic: Â Acceleration |

Â 70%

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: Â Acceleration |

Â 67%

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A particle moving on a curved path possesses a velocity of \(3\) m/s towards the north at an instant. After \(10\) s, it is moving with speed \(4\) m/s towards the west. The average acceleration of the particle is:

1. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) south to east. |

2. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) west to north. |

3. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) east to north. |

4. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) south to west. |

Subtopic: Â Acceleration |

Â 68%

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A particle is moving along a curve. Select the correct statement.

1. | If its speed is constant, then it has no acceleration. |

2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |

3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |

4. | If its speed is constant, its acceleration is perpendicular to its velocity. |

Subtopic: Â Acceleration |

Â 69%

From NCERT

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A particle is moving eastwards with velocity of \(5\) m/s. In \(10\) seconds the velocity changes to \(5\) m/s northwards. The average acceleration in this time is?

1. | zero |

2. | \(\frac{1}{\sqrt{2}}~ \text{m/s}^2\) toward north-west |

3. | \(\frac{1}{\sqrt{2}}~\text{m/s}^2\) toward north-east |

4. | \(\frac{1}{2}~\text{m/s}^2 \) toward north-west |

Subtopic: Â Acceleration |

Â 64%

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