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. \(6\ \text{m}\)

An elevator car, whose floor-to-ceiling distance is equal to \(2.7~\text{m}\), starts ascending with constant acceleration of \(1.2~\text{ms}^{-2}\). \(2\ \text{s}\)  after the start, a bolt begins falling from the ceiling of the car. The free-fall time of the bolt is: 
1. \(\sqrt{0.54}~\text{s}\)
2. \(\sqrt{6}~\text{s}\)
3. \(0.7~\text{s}\)
4. \(1~\text{s}\)

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. \(15\ \text{m/s}^2\)$\mathrm{}$

Two trains travelling on the same track are approaching each other with equal speeds of \(40\ \text{m/s}\). The drivers of the trains begin to decelerate simultaneously when they are just \(2.0\ \text{km}\) apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be:

1. \(11.8\ \text{m/s}^2\)
2. \(11.0\ \text{m/s}^2\)
3. \(1.6\ \text{m/s}^2\)
4. \(0.8\ \text{m/s}^2\)

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. \(0.5\)

A body starts from rest. What is the ratio of the distance travelled by the body during the \(4^{th}\) and \(3^{rd}\) second:

1. \(\dfrac 75\)

2. \(\dfrac 57\)

3. \(\dfrac 73\)

4. \(\dfrac 37\)

The acceleration \(a\) in m/s² of a particle is given by $a=3t^2+2t+2$ where t is the time. If the particle starts out with a velocity, \(u=2\) m/s at t = 0, then the velocity at the end of \(2\) seconds will be:
1. \(12\) m/s
2. \(18\) m/s
3. \(27\) m/s
4. \(36\) m/s