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The figure shows the displacement-time graph of a particle moving on the x-axis. Then,

1. | the particle is continuously going in a positive x-direction. |

2. | the particle is at rest. |

3. | the velocity increases up to a time \(t_0\), and then becomes constant. |

4. | the particle moves at a constant velocity up to a time \(t_0\), and then stops. |

Subtopic: Â Graphs |

Â 70%

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A person travelling on a straight line moves with a uniform velocity \(v_1,\) for some time and with uniform velocity \(v_2\) for the next equal time. The average velocity \(v\) is given by:

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

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

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

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

Subtopic: Â Average Speed & Average Velocity |

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A person traveling on a straight line moves with a uniform velocity \(v_1\) for a distance \(x\) and with a uniform velocity \(v_2,\) for the next equal distance. The average velocity \(v\) is given by:

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

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

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

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

Subtopic: Â Average Speed & Average Velocity |

Â 69%

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A stone is released from an elevator going up with an acceleration \(a.\) The acceleration of the stone after the release is:

1. \(a\) upward

2. \((g-a)\) upward

3. \((g-a)\) downward

4. \(g\) downward

Subtopic: Â Uniformly Accelerated Motion |

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A person standing near the edge of the top of a building throws two balls \(A\) and \(B.\) The ball \(A\) is thrown vertically upward and \(B\) is thrown vertically downward with the same speed. The ball \(A\) hits the ground with a speed \(v_A\) and the ball \(B\) hits the ground with a speed \(v_B.\) We have:

1. | \(v_A>v_B\) |

2. | \(v_A<v_B\) |

3. | \(v_A=v_B\) |

4. | the relation between \(v_A\) and \(v_B\) depends on height of the building above the ground |

Subtopic: Â Uniformly Accelerated Motion |

Â 71%

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A particle moves along the \(x\text-\)axis as:

\(x=u(t-2)+a(t-2)^2\)

a. | the initial velocity of the particle is \(u.\) |

b. | the acceleration of the particle is \(a.\) |

c. | the acceleration of the particle is \(2a.\) |

d. | at \(t=2\) s particle is at the origin. |

Choose the correct option:

1. | (a) and (b) | 2. | (b) and (c) |

3. | (c) and (d) | 4. | (a) and (d) |

Subtopic: Â Acceleration |

Â 56%

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Pick the correct statements:

a. | Average speed of a particle in a given time is never less than the magnitude of the average velocity. |

b. | \(|\frac{d \vec{v}}{d t}| \neq 0\) but \(\frac{d}{d t}|\vec{v}|=0.\) | It is possible to have a situation in which

c. | The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. |

d. | The average velocity of a particle moving in a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed) |

Choose the correct option:

1. | (a), (b) and (c) |

2. | (b), (c) and (d) |

3. | (a) and (b) |

4. | (b) and (c) |

Subtopic: Â Average Speed & Average Velocity |

Â 63%

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An object may have:

a. | varying speed without having a varying velocity. |

b. | varying velocity without having varying speed. |

c. | non-zero acceleration without having a varying velocity. |

d. | non-zero acceleration without having varying speed. |

Choose the correct option:

1. | (a) and (b) |

2. | (b) and (c) |

3. | (c) and (d) |

4. | (b) and (d) |

Subtopic: Â Instantaneous Speed & Instantaneous Velocity |

Â 65%

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Mark the correct statements for a particle going on a straight line:

(a) | if the velocity and acceleration have opposite sign, the object is slowing down. |

(b) | if the position and velocity have opposite sign, the particle is moving towards the origin. |

(c) | if the velocity is zero at an instant, the acceleration should also be zero at that instant. |

(d) | if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval. |

Choose the correct option:

1. | (a), (b) and (c) | 2. | (a), (b) and (d) |

3. | (b), (c) and (d) | 4. | all of these |

Subtopic: Â Acceleration |

Â 65%

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The velocity of a particle is zero at t = 0.

(a) The acceleration at t = 0 must be zero

(b) The acceleration at t = 0 may be zero

(c) If the acceleration is zero from t = 0 to t = 10 s, the speed is also zero in this interval

(d) If the speed is zero from t = 0 to t = 10s the acceleration is also zero in this interval

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (c), (d) and (a)

4. (a), (b) and (d)

Subtopic: Â Acceleration |

Â 68%

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