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. \(128~\text{m}\)

A car moving with a velocity of \(10\ \text{m/s}\) can be stopped by the application of a constant force \(F\) in a distance of \(20\ \text{m}\). If the velocity of the car is \(30\ \text{m/s}\), it can be stopped by this force in:

1. \(\dfrac {20}{3} \ \text{𝑚}\)

2. \(20\ \text{m}\)

3. \(60\ \text{m}\)

4. \(180\ \text{m}\)

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 boggy of a uniformly moving train is suddenly detached from the train and stops after covering some distance. The distance covered by the boggy and the distance covered by the train in the same time has relation:

1. Both will be equal
2. First will be half of second
3. First will be \(1/4\) of second
4. No definite ratio

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. \(\dfrac 37\)