A particle moves along the x-axis as \({x}=4({t}-2)+{a}({t}-2)^2.\)Which of the following is true? 

1.	The initial velocity of the particle is \(4\)
2.	The acceleration of the particle is \(2a\)
3.	The particle is at the origin at \( t = 0\)
4.	None of these

 

A body starting from rest moves with constant acceleration. The ratio of the distance covered by the body during the \(5^{th}\) second to that covered in \(5\) second is:

1. \(9/25\)
2. \(3/5\)
3. \(25/9\)
4. \(1/25\)

Two trains, each \(50\) m long, are travelling in the opposite direction with velocities \(10\) m/s and \(15\) m/s. The time of crossing is:
1. \(10\) sec
2. \(4\) sec
3. \(2\sqrt{3}\) sec
4. \(4\sqrt{3}\) sec

A \(120\ \text{m}\) long train is moving in a direction with speed \(20\ \text{m/s}\). A train \(B\), moving with \(30\ \text{m/s}\) in the opposite direction and \(130\ \text{m}\) long, crosses the first train in a time:

1.  \(4\ \text{s}\)
2.  \(36\ \text{s}\)
3.  \(38\ \text{s}\)
4.  \(5\ \text{s}\)

A \(210\) meter long train is moving due north at a speed of \(25\ \text{m/s}\). A small bird is flying due South a little above the train with a speed of \(5\ \text{m/s}\). The time taken by the bird to cross the train is:

1. \(6\ \text{s}\)
2. \(7\ \text{s}\)
3. \(9\ \text{s}\)
4. \(10\ \text{s}\)

A police jeep is chasing with a velocity of \(45\text{ km/h}\) a thief in another jeep moving with a velocity of \(153\text{ km/h}.\) Police fire a bullet with a muzzle velocity of \(180\text{ m/s}.\) The velocity with which it will strike the car of the thief is:

1.  \(150\text{ m/s}\)
2.  \(27\text{ m/s}\)
3.  \(450\text{ m/s}\)
4.  \(250\text{ m/s}\)

A train of \(150\) meter length is going towards the north direction at a speed of \(10\ \text{m/s}\). A parrot flies at the speed of \(5\ \text{m/s}\) towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is:

1. \(12\) seconds

2. \(8\) seconds

3. \(15\) seconds

4. \(10\) seconds

The distance between two particles is decreasing at the rate of \(6\) m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of \(4\) m/sec. It can be concluded that particles' speeds could be:
1. \(5\) m/sec, \(1\) m/sec
2. \(4\) m/sec, \(1\) m/sec
3. \(4\) m/sec, \(2\) m/sec
4. \(5\) m/sec, \(2\) m/sec

An express train is moving with a velocity \(v_1\). Its driver finds another train is moving on the same track in the same direction with velocity \(v_2\). To escape collision, driver applies a retardation \(a\) on the train. The minimum time of escaping collision will be:

1. \(t = \dfrac{v_1 - v_2}{a}\)

2. \(t_1 = \dfrac{v_1^2 - v_2^2}{2}\)

3. Both

4. None of the above

A stone falls from a balloon that is descending at a uniform rate of \(12\ \text{m/s}\). The displacement of the stone from the point of release after \(10\ \text{s}\) is:

1. \(490\ \text{m}\)
2. \(510\ \text{m}\)
3. \(610\ \text{m}\)
4. \(725\ \text{m}\)