Q. No.The motion of a particle is given by the equation \(S = \left(3 t^{3} + 7 t^{2} + 14 t + 8 \right) \text{m} ,\) The value of the acceleration of the particle at \(t=1~\text{s}\) is:
| 1. | \(10\) m/s2 | 2. | \(32\) m/s2 |
| 3. | \(23\) m/s2 | 4. | \(16\) m/s2 |
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A body is moving along a straight line according to the equation of motion, \(x= t^{2} - 3 t + 4\), where \(x\) is in metre and \(t\) is in seconds. What is the acceleration of the body when it comes to rest?
| 1. | zero | 2. | \(2~\text{m/s}^2\) |
| 3. | \(\frac{3}{2}~\text{m/s}^2\) | 4. | \(1~\text{m/s}^2\) |
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The position \(x\) of a particle varies with time \(t\) as \(x=at^2-bt^3\). The acceleration of the particle will be zero at time \(t\) equal to:
| 1. | \(\dfrac{a}{b}\) | 2. | \(\dfrac{2a}{3b}\) |
| 3. | \(\dfrac{a}{3b}\) | 4. | zero |
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A particle moves along a straight line such that its displacement at any time \(t\) is given by \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is:
1. \(4\) ms-1
2. \(-12\) ms−1
3. \(42\) ms−1
4. \(-9\) ms−1
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The acceleration \(a\) in m/s2 of a particle is given by where t is the time. If the particle starts out with a velocity, \(u=2\) m/s at t = 0, then the velocity at the end of \(2\) seconds will be:
1. \(12\) m/s
2. \(18\) m/s
3. \(27\) m/s
4. \(36\) m/s
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If the velocity of a particle is given by \(v = (180-16x)^{1/2}~\text{m/s} \), then its acceleration will be:
1. zero
2. \(8\text{ m/s}^2\)
3. \(-8\text{ m/s}^2\)
4. \(4\text{ m/s}^2\)
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When the velocity of a body is variable, then:
| 1. | its speed may be constant |
| 2. | its acceleration may be constant |
| 3. | its average acceleration may be constant |
| 4. | all of the above |
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A particle moves a distance \(x\) in time \(t\) according to equation \(x = (t+5)^{-1}\). The acceleration of the particle is proportional to:
| 1. | \((\text{velocity})^{\frac{3}{2}}\) | 2. | \((\text{distance})^2\) |
| 3. | \((\text{distance})^{-2}\) | 4. | \((\text{velocity})^{\frac{2}{3}}\) |
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A body is projected vertically in the upward direction from the surface of the earth. If the upward direction is taken as positive, then the acceleration of the body during its upward and downward journey is:
| 1. | Positive, negative | 2. | Negative, negative |
| 3. | Positive, positive | 4. | Negative, positive |
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The velocity \(v\) of an object varies with its position \(x\) on a straight line as \(v=3\sqrt{x}.\) Its acceleration versus time \((a\text-t)\) graph is best represented by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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