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

A particle moves along a straight line such that its displacement at any time \(t\) is given by \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is:
1.  \(4\) ms^-1
2.  \(-12\) ms⁻¹
3.  \(42\) ms⁻¹
4.   \(-9\) ms⁻¹

If a body starts from rest and travels \(120\ \text{cm}\) in the \(6^{th}\) second, then what is the acceleration:

1. \(0.20\ \text{m/s}^2\)
2. \(0.027\ \text{m/s}^2\)
3. \(0.218\ \text{m/s}^2\)
4. \(0.03\ \text{m/s}^2\)

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. \(2880\ \text{m}\)