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

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

A car moving with a speed of 40 km/h can be stopped by applying brakes for atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance ?

1. 8 m

2. 2 m

3. 4 m

4. 6 m

An elevator car, whose floor to ceiling distance is equal to \(2.7~\text{m}\), starts ascending with constant acceleration of \(1.2~\text{ms}^{-2}\). \(2\) sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is: 
1. \(\sqrt{0.54}~\text{s}\)
2. \(\sqrt{6}~\text{s}\)
3. \(0.7~\text{s}\)
4. \(1~\text{s}\)

The displacement is given by $x=2t^2+t+5$, the acceleration at $t=2s$ is 

1. $4m/s^2$

2. $8m/s^2$

3. $10m/s^2$

4. $15m/s^2$

Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be 

1. 11.8 m/s²

2. 11.0 m/s²

3. 1.6 m/s²

4. 0.8 m/s²

A body moves from rest with a constant acceleration of 5 m/s². Its instantaneous speed (in m/s) at the end of 10 sec is  

1. 50

2. 5

3. 2

4. 0.5

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation 

1. Both will be equal

2. First will be half of second

3. First will be 1/4 of second

4. No definite ratio

A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second 

1. $\frac{7}{5}$

2. $\frac{5}{7}$

3. $\frac{7}{3}$

4. $\frac{3}{7}$ 

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 \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is: