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 \(𝑠 = 2 𝑡^2 + 2 𝑡 + 4\) where \(s\) is in meters and \(t\) in seconds. The acceleration of the particle is:

1. \(2\ \text{m/s}^2\)
2. \(4\ \text{m/s}^2\)
3. \(6\ \text{m/s}^2\)
4. \(8\ \text{m/s}^2\)

A body \(A\) starts from rest with an acceleration \(a_1\). After \(2\) seconds, another body B starts from rest with an acceleration \(a_2\). If they travel equal distances in the \(5^{th}\) second, after the start of \(A\), then the ratio \(a_1: a_2\)  is equal to:

1. \(5: 9\)
2. \(5: 7\)
3. \(9: 5\)
4. \(9: 7\)

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

1. \(10×10^4\ \text{m/s}^2\)

2. \(12×10^4\ \text{m/s}^2\)$\mathrm{}$

3. \(13.5×10^4\ \text{m/s}^2\)$\mathrm{}$

4. \(15×10^4\ \text{m/s}^2\)$\mathrm{}$

A particle starts from rest, accelerates at \(2\ \text{m/s}^2\) for \(10\ \text{s}\) and then goes for constant speed for \(30\ \text{s}\) and then decelerates at \(4\ \text{m/s}^2\) till it stops. What is the distance travelled by it?

1. \(750\ \text{m}\)
2. \(800\ \text{m}\)
3. \(700\ \text{m}\)
4. \(850\ \text{m}\)