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. \(8\)

Two cars \(A\) and \(B\) are at rest at the same point initially. If \(A\) starts with a uniform velocity of \(40\ \text{m/s}\) and \(B\) starts in the same direction with a constant acceleration of \(4\ \text{m/s}^2\), then \(B\) will catch \(A\) after how much time?

1. \(10\ \text{s}\)
2. \(20\ \text{s}\)
3. \(30\ \text{s}\)
4. \(35\ \text{s}\)

The motion of a particle is described by the equation \(𝑥 = 𝑎 + 𝑏 𝑡^ 2\) where \(a = 15\ \text{cm}\) and \(b = 3\ \text{cm/s}^2\). Its instantaneous velocity at time \(3\) seconds will be:

1. \(36\ \text{cm/s}\)
2. \(18\ \text{cm/s}\)
3. \(16\ \text{cm/s}\)
4. \(32\ \text{cm/s}\)

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. \(8\ \text{m/s}^2\)

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 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

An object accelerates from rest to a velocity of \(27.5\ \text{m/s}\) in \(10\ \text{s}\). Then find the distance covered by the object in the next \(10\ \text{s}\):

1. \(550\ \text{m}\)
2. \(137.5\ \text{m}\)
3. \(412.5\ \text{m}\)
4. \(275\ \text{m}\)

The speeds of two identical cars are \(u\) and \(4u\) at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is:

1. \(1 : 1\)
2. \(1 : 4\)
3. \(1 : 8\)
4. \(1 : 16\)

A car, starting from rest, accelerates at the rate \(f\) through a distance \(S\), then continues at a constant speed for time \(t\) and then decelerates at the rate \(\frac f2\) to come to rest. If the total distance traversed is \(15\ \text{S}\), then:

1. \(S = \frac{1}{2}ft^2\)
2. \(S = \frac{1}{4}ft^2\)
3. \(S = \frac{1}{72}ft^2\)
4. \(S = \frac{1}{6}ft^2\)