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

The displacement of a particle starting from rest (at \(t = 0\)) is given by \(𝑠 = 6 𝑡^ 2 − 𝑡^ 3\). The time in seconds at which the particle will attain zero velocity again is:  

1. \(2\)
2. \(4\)
3. \(6\)
4. \(8\)

A body is moving according to the equation \(𝑥 = 𝑎 𝑡 + 𝑏 𝑡^ 2 − 𝑐 𝑡^ 3\) where \(x\) is the displacement, and \(a,\ b\) and \(c\) are constants. The acceleration of the body is:

1. \(𝑎 + 2 𝑏 𝑡\) 
2. \(2 𝑏 + 6 𝑐 𝑡  \)
3. \(2 𝑏 − 6 𝑐 𝑡  \)
4. \(3 𝑏 − 6 𝑐 𝑡^ 2  \)

The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is: 

The average velocity of a body moving with uniform acceleration travelling a distance of \(3.06\ \text{m}\) is \(0.34\ \text{ms}^{–1}\). If the change in velocity of the body is \(0.18\ \text{ms}^{–1}\) during this time, its uniform acceleration is:

1. \(0.01\ \text{ms}^{–2}\)

2. \(0.02\ \text{ms}^{–2}\)

3. \(0.03\ \text{ms}^{–2}\)

4. \(0.04\ \text{ms}^{–2}\)

The displacement of a particle is proportional to the cube of the time elapsed. How does the acceleration of the particle depends on time obtained?

1. \(𝑎 ∝ t^ 2 \)
2. \(𝑎 ∝ 𝑡^ 4 \)
3. \(𝑎 ∝ 𝑡 ^3\)
4. \(𝑎 ∝ 𝑡  \)

Starting from rest, the acceleration of a particle is \(𝑎 = 2 ( 𝑡 − 1 )\). The velocity of the particle at \(𝑡 = 5\ \text{𝑠}\) is:

1.  \(15\ \text{m/s}\)
2.  \(25\ \text{m/s}\)
3.  \(5\ \text{m/s}\)
4.  None of these

A particle moves along the x-axis as \({x}=4({t}-2)+{a}({t}-2)^2.\)Which of the following is true? 

A \(210\) meter long train is moving due north at a speed of \(25\ \text{m/s}\). A small bird is flying due South a little above the train with a speed of \(5\ \text{m/s}\). The time taken by the bird to cross the train is:

1. \(6\ \text{s}\)
2. \(7\ \text{s}\)
3. \(9\ \text{s}\)
4. \(10\ \text{s}\)

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is 

1. 2100 m/sec² downwards

2. 2100 m/sec² upwards

3. 1400 m/sec²

4. 700 m/sec²