Q. No.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 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 m/s, then its acceleration will be:
| 1. | zero | 2. | \(8\) m/s2 |
| 3. | \(-8\) m/s2 | 4. | \(4\) m/s2 |
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. | \(1:5:6\) |
A body is thrown vertically up from the ground. It reaches a maximum height of \(100\) m in \(5\) s. After what time will it reach the ground from the position of maximum height?
| 1. | \(1.2\) s | 2. | \(5\) s |
| 3. | \(10\) s | 4. | \(25\) s |
If a body is thrown up with the velocity of \(15\) m/s, then the maximum height attained by the body is: (assume \(g = 10\) m/s2)
1. \(11.25\) m
2. \(16.2\) m
3. \(24.5\) m
4. \(7.62\) m
If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds, the time of the travel is:
1. \(6\) sec
2. \(5\) sec
3. \(4\) sec
4. \(3\) sec
A particle moving in a straight line covers half the distance with a speed of \(3~\text{m/s}\). The other half of the distance is covered in two equal time intervals with speeds of \(4.5~\text{m/s}\) and \(7.5~\text{m/s}\) respectively. The average speed of the particle during this motion is:
| 1. | \(4.0~\text{m/s}\) | 2. | \(5.0~\text{m/s}\) |
| 3. | \(5.5~\text{m/s}\) | 4. | \(4.8~\text{m/s}\) |
A particle starts from rest. Its acceleration \((a)\) versus time \((t)\) is as shown in the figure. The maximum speed of the particle will be:
1. \(110~\text{m/s}\)
2. \(55~\text{m/s}\)
3. \(550~\text{m/s}\)
4. \(660~\text{m/s}\)
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