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 m/s
2. 55 m/s
3. 550 m/s
4. 660 m/s