The velocity of a particle changes when:

1. Direction of velocity changes
2. Magnitude of velocity changes
3. Both of above
4. None of the above

The motion of a particle is described by the equation \(u = at\), where \(u\) is the velocity and \(a\) is a constant. The distance travelled by the particle in the first \(4\) seconds:

1. \(4 a\)
2. \(12 a\)
3. \(6 a\)
4. \(8 a\)

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 equation of displacement for any particle is \(𝑠 = 3 𝑡^ 3 + 7 𝑡^ 2 + 14 𝑡 + 8\ \text{m}\). Its acceleration at time \(t = 1\) second is:

1. \(10\ \text{m/s}^2\)
2. \(16\ \text{m/s}^2\)
3. \(25\ \text{m/s}^2\)
4. \(32\ \text{m/s}^2\)

The position of a particle moving along the \(x\)-axis at certain times is given below:

Which of the following describes the motion correctly?  
1. Uniform, accelerated
2. Uniform, decelerated
3. Non-uniform, accelerated
4. There is not enough data for generalisation

Consider the acceleration, velocity and displacement of a tennis ball as it falls to the ground and bounces back. Directions of which of these changes in the process ?

1. Velocity only

2. Displacement and velocity

3. Acceleration, velocity and displacement

4. Displacement and acceleration

The displacement of a particle, moving in a straight line, is given by $s=2t^2+2t+4$ where s is in metres and t in seconds. The acceleration of the particle is 

1. 2 m/s²

2. 4 m/s²

3. 6 m/s²

4. 8 m/s²

A body A starts from rest with an acceleration a₁. After 2 seconds, another body B starts from rest with an acceleration a₂. If they travel equal distances in the 5th second, after the start of A, then the ratio a₁: a₂  is equal to:

1. 5: 9

2. 5: 7

3. 9: 5

4. 9: 7

The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be  

1. $10\times {10}^4$ m/s²

2. $12\times {10}^4$ m/s²

3. $13.5\times {10}^4$ m/s²

4. $15\times {10}^4$ m/s²