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. \(8\text{ m/s}^2\)
3. \(-8\text{ m/s}^2\)
4. \(4\text{ m/s}^2\)

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: 

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: 

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?

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. \(4.8~\text{m/s}\)