A particle moves along the x-axis as $\mathrm{x}=4(\mathrm{t}-2)+\mathrm{a}{(\mathrm{t}-2)}^2$. 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 distance covered by the body during the 5th sec to that covered in 5 sec 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 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time  

1.  4 s
2.  36 s
3.  38 s
4.  5 s

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

(1) 6 s

(2) 7 s

(3) 9 s

(4) 10 s

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

1.  150 m/s
2.  27 m/s
3.  450 m/s
4.  250 m/s

A train of 150 meter length is going towards north direction at a speed of 10 m/sec. A parrot flies at the speed of 5 m/sec towards south direction parallel to the railway track. The time taken by the parrot to cross the train is 

(1) 12 sec

(2) 8 sec

(3) 15 sec

(4) 10 sec

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 v₁. Its driver finds another train is moving on the same track in the same direction with velocity v₂. To escape collision, driver applies a retardation 'a' on the train. The minimum time of escaping collision will be 

1.  $t=\frac{v_1-v_2}{a}$
2.  $t_1=\frac{v_1^2-v_2^2}{2}$
3.  None
4.  Both

A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The displacement of the stone from the point of release after 10 sec is

(1) 490 m

(2) 510 m

(3) 610 m

(4) 725 m