A body of mass \(10\ \text{kg}\) is moving with a constant velocity of \(10\ \text{m/s}\). When a constant force acts for \(4\ \text{s}\) on it, it moves with a velocity \(2\ \text{m/s}\) in the opposite direction. The acceleration produced in it is:

1. \(3\ \text{m/s}^2\)
2. \(-3\ \text{m/s}^2\)
3. \(0.3\ \text{m/s}^2\)
4. \(-0.3\ \text{m/s}^2\)

A body starts from rest from the origin with an acceleration of \(6~\text{m/s}^2\) along the \(x\text-\)axis and \(8~\text{m/s}^2\) along the \(y\text-\)axis. Its distance from the origin after \(4\) seconds will be:
1. \(56~\text{m}\)
2. \(64~\text{m}\)
3. \(80~\text{m}\)
4. \(128~\text{m}\)

The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:

A car moving with a speed of \(40\ \text{km/h}\) can be stopped by applying the brakes for at least \(2\ \text{m}\). If the same car is moving with a speed of \(80\ \text{km/h}\), what is the minimum stopping distance?

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

The displacement is given by \(𝑥 = 2 𝑡^ 2 + 𝑡 + 5 ,\) the acceleration at \(𝑡 = 2 \ \text{s}\) is:

1. \(4\ \text{m/s}^2\)
2. \(8\ \text{m/s}^2\)
3. \(10\ \text{m/s}^2\)$\mathrm{}$
4. \(15\ \text{m/s}^2\)$\mathrm{}$

A body moves from rest with a constant acceleration of \(5\ \text{m/s}^2\). Its instantaneous speed (in m/s) at the end of \(10\ \text{s}\) is  

1. \(50\)
2. \(5\)
3. \(2\)
4. \(0.5\)

If a car at rest accelerates uniformly to a speed of \(144\ \text{km/h}\) in \(20\ \text{s}\). Then it covers a distance of:

1. \(20\ \text{m}\)
2. \(400\ \text{m}\)
3. \(1440\ \text{m}\)
4. \(2880\ \text{m}\)

If a train travelling at \(72\ \text{km/h}\) is to be brought to rest in a distance of \(200\) metres, then its retardation should be:

1. \(20\ \text{ms}^{–2}\)
2. \(10\ \text{ms}^{–2}\)
3. \(2\ \text{ms}^{–2}\)
4. \(1\ \text{ms}^{–2}\) 

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. \(35\ \text{s}\)