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

(1) The initial velocity of particle is 4

(2) The acceleration of particle is 2a

(3) The particle is at origin at t = 0

(4) None of these

Concept Questions :-

Instantaneous speed and instantaneous velocity
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Difficulty Level:

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

Concept Questions :-

Uniformly accelerated motion
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Difficulty Level:

What determines the nature of the path followed by the particle

(1) Speed

(2) Velocity

(3) Acceleration

(4) Both (2) and (3)

Concept Questions :-

Instantaneous speed and instantaneous velocity
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Difficulty Level:

Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s and 15 m/s. The time of crossing is

(1) 10 s

(2) 4 s

(3) $2\sqrt{3}s$

(4) $4\sqrt{3}s$

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

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

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

A 210 meter long train is moving due North at a speed  of 25m/s. A small bird is flying due South a little above the train with speed 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

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

A police jeep is chasing with, velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity 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

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

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

Concept Questions :-

Relative motion in 1-D
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Difficulty Level:

A boat is moving with velocity of $3\stackrel{^}{i}+4\stackrel{^}{j}$ in river and water is moving with a velocity of $-3\stackrel{^}{i}-4\stackrel{^}{j}$ with respect to ground. Relative velocity of boat with respect to water is :

(1) $-6\stackrel{^}{i}-8\stackrel{^}{j}$

(2) $6\stackrel{^}{i}+8\stackrel{^}{j}$

(3) $8\stackrel{^}{j}$

(4) $6\stackrel{^}{i}$

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Difficulty Level:

The distance between two particles is decreasing at the rate of 6 m/sec. If these particles travel with same initial speeds and in the same direction, then the separation increases at the rate of 4 m/sec. The particles have speeds as

(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