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 |
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 |
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. | \(1~\text{m/s}^2\) |
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 |
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
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 |
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. | \(8\) m/s2 |
3. | \(-8\) m/s2 | 4. | \(4\) m/s2 |
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. | \((\text{velocity})^{\frac{2}{3}}\) |
If a particle has negative velocity and negative acceleration, its speed:
1. increases
2. decreases
3. remains the same
4. zero