Q. No.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
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 |
A student is standing at a distance of \(50\) metres from the bus. As soon as the bus begins its motion with an acceleration of \(1\) ms–2, the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is:
1. \(5\) ms–1
2. \(8\) ms–1
3. \(10\) ms–1
4. \(12\) ms–1
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 |
Two trains, each \(50\) m long, are travelling in the opposite direction with velocities \(10\) m/s and \(15\) m/s. The time of crossing is:
1. \(10\) sec
2. \(4\) sec
3. \(2\sqrt{3}\) sec
4. \(4\sqrt{3}\) sec
The distance between two particles is decreasing at the rate of \(6\) m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of \(4\) m/sec. It can be concluded that particles' speeds could be:
1. \(5\) m/sec, \(1\) m/sec
2. \(4\) m/sec, \(1\) m/sec
3. \(4\) m/sec, \(2\) m/sec
4. \(5\) m/sec, \(2\) m/sec
A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is:
| 1. | Equal to the time of fall. |
| 2. | Less than the time of fall. |
| 3. | Greater than the time of fall. |
| 4. | Twice the time of fall. |
A body starts to fall freely under gravity. The distances covered by it in the first, second and third second will be in the ratio:
| 1. | \(1:3:5\) | 2. | \(1:2:3\) |
| 3. | \(1:4:9\) | 4. | \(1:5:6\) |
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