The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^2-{\mathrm{dt}}^4$. The initial velocity and acceleration are, respectively:

1.	\(\mathrm{b}, ~\mathrm{-4d}\)	2.	\(\mathrm{-b},~ \mathrm{2c}\)
3.	\(\mathrm{b}, ~\mathrm{2c}\)	4.	\(\mathrm{2c}, ~\mathrm{-2d}\)

The acceleration ‘a’ in m/s² of a particle is given by $a=3t^2+2t+2$ 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 $\mathrm{S}={\mathrm{t}}^3-6{\mathrm{t}}^2+3\mathrm{t}+4$ metres. The velocity when the acceleration is zero is:

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. \(\frac{a}{b}\)
2. \(\frac{2a}{3b}\)
3. \(\frac{a}{3b}\)
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 $v={(180-16x)}^{1/2}$ 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: 

A body starts to fall freely under gravity. The distances covered by it in 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 seconds. After what time will it reach the ground from the position of maximum height?
1. 1.2 sec
2. 5 sec
3. 10 sec
4. 25 sec

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