The displacement \(x\) of a particle moving in one dimension under the action of a constant force is related to time t by the equation , where \(x\) is in metres and \(t\) is in seconds. What is the displacement of the particle from t = 0 s to t = 6 s?
1. \(0\)
2. \(12\) m
3. \(6\) m
4. \(18\) m
The acceleration \(a\) (in ) of a body, starting from rest varies with time \(t\) (in \(\mathrm{s}\)) as per the equation \(a=3t+4.\) The velocity of the body at time \(t=2\) \(\mathrm{s}\) will be:
1. | \(10~\text{ms}^{-1}\) | 2. | \(18~\text{ms}^{-1}\) |
3. | \(14~\text{ms}^{-1}\) | 4. | \(26~\text{ms}^{-1}\) |
A point moves in a straight line under the retardation \(av^2\). If the initial velocity is \(u,\) the distance covered in \(t\) seconds is:
1. \((aut)\)
2. \(\frac{1}{a}\mathrm{ln}(aut)\)
3. \(\frac{1}{a}\mathrm{ln}(1+aut)\)
4. \(a~\mathrm{ln}(aut)\)
The relation between time and distance is given by , where α and β are constants. The retardation, as calculated based on this equation, will be (assume v to be velocity):
1.
2.
3.
4.
The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:
1. | \(b, -4d\) | 2. | \(-b,2c\) |
3. | \(b, ~2c\) | 4. | \(2c, -2d\) |
An elevator car, whose floor to ceiling distance is equal to \(2.7~\text{m}\), starts ascending with constant acceleration of \(1.2~\text{ms}^{-2}\). \(2\) sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:
1. \(\sqrt{0.54}~\text{s}\)
2. \(\sqrt{6}~\text{s}\)
3. \(0.7~\text{s}\)
4. \(1~\text{s}\)
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
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 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 |
The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is:
1. | \(24\) metres | 2. | \(12\) metres |
3. | \(5\) metres | 4. | zero |