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

1. 2 $\mathrm{m}/{\mathrm{s}}^{2}$

2. 3 $\mathrm{m}/{\mathrm{s}}^{2}$

3. 4 $\mathrm{m}/{\mathrm{s}}^{2}$

4. Zero

Subtopic: Acceleration |

86%

From NCERT

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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: Acceleration |

81%

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

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

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

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

Subtopic: Acceleration |

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: Acceleration |

74%

From NCERT

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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: Acceleration |

71%

From NCERT

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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: Acceleration |

70%

From NCERT

NEET - 2016

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A particle moves in space such that:

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

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

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

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

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

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

Subtopic: Acceleration |

67%

From NCERT

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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: Acceleration |

68%

From NCERT

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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 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° south to east |

2. | 0.25 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° west to north |

3. | 0.5 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° east to north |

4. | 0.5 $\mathrm{m}/{\mathrm{s}}^{2}$, 37° south to west |

Subtopic: Acceleration |

68%

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

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

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

Subtopic: Acceleration |

63%

From NCERT

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