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 

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. \(850\ \text{m}\)

The engine of a motorcycle can produce a maximum acceleration of \(5\ \text{m/s}^2\). Its brakes can produce a maximum retardation of \(10\ \text{m/s}^2\). What is the minimum time in which it can cover a distance of \(1.5\ \text{km}\)?

1. \(30\ \text{s}\)
2. \(15\ \text{s}\)
3. \(10\ \text{s}\)
4. \(5\ \text{s}\)

A car, moving with a speed of \(50\ \text{km/h}\), can be stopped by the brakes after at least \(6\ \text{m}\). If the same car is moving at a speed of \(100\ \text{km/h}\), the minimum stopping distance is:

1. \(6\ \text{m}\)
2. \(12\ \text{m}\)
3. \(18\ \text{m}\)
4. \(24\ \text{m}\)

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