A cat is situated at point A (0, 3, 4) and a rat is situated at point B (5, 3, -8). The cat is free to move but the rat is always at rest. The minimum distance traveled by the cat to catch the rat is:

1. 5 unit

2. 12 unit

3. 13 unit

4. 17 unit

Subtopic:  Position & Displacement |
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Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance of 120 m. Which of the following statements is correct?

   

1. The balls can never meet.

2. The balls can meet if the ball B is thrown 1 s later.

3. The two balls meet at a height of 45 m.

4. None of the above

Subtopic:  Relative Motion |
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A body is projected at an angle of 30° with the horizontal with a speed of 30 m/s. What is the angle made by the velocity vector with the horizontal after 1.5 sec? (g = 10m/s2)

1. 0°

2. 30°

3. 60°

4. 90°

Subtopic:  Projectile Motion |
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A particle moves along the positive branch of the curve y = x22 where x = t22, & x and y are measured in metres and in seconds respectively. At = 2s, the velocity of the particle will be

1. (2i^-4j^ )m/s

2. (4i^+2j^ )m/s

3. (2i^+4j^ )m/s

4. (4i^-2j^ )m/s

Subtopic:  Speed & Velocity |
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A deer wants to save her life from a lion. The lion follows a path whose equation is x2+y2=16. For saving her life, the deer needs to move on a path whose equation will be

1. x2+y2=4

2. x2+y2=16

3. x2+y2-64=0

4. Both (1)and(3) are correct

Subtopic:  Circular Motion |
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A particle rotates in a circular path starting from rest. If angular acceleration is 4 rad/s2, then the time after which angle between net acceleration and tangential acceleration becomes 45° is

1. 0.5 s

2. 0.25 s

3. 2 s

4. 4 s

Subtopic:  Circular Motion |
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The position of a moving particle at time t is r=3i^+4t2j^-t3k^. Its displacement during the time interval t = 1 sec to t = 3 sec will be

1. j^-k^

2. 3i^-4j^-k^

3. 9i^+36j^-27k^

4. 32j^-26k^

Subtopic:  Position & Displacement |
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An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2m, its velocity is –(4 m/s)j^. What is the object's acceleration when it is at y = 2m?

1. -(8m/s2) j^

2. -(8m/s2) i^

3. -(4m/s2) j^

4. -(4m/s2) i^

Subtopic:  Circular Motion |
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A particle has an initial velocity u=(4i^-5j^) m/s and it is moving with an acceleration a=14i^+15j^m/s2. Velocity of the particle at t =2s will be

1. (6i^-4j^)m/s

2. (4.5i^-4.5j^)m/s

3. (4.5i^-4.6j^)m/s

4. (6i^-4.6j^)m/s

Subtopic:  Uniformly Accelerated Motion |
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To the captain of a ship A travelling with velocity vA=(3i^-4j^) km/h, a second ship B appears to have a velocity vB=5i^+12j^ km/h. What is the true velocity of the ship B?

1. 2i^+16j^ km/h

2. 13i^+8j^ km/h

3. -2i^-16j^ km/h

4. none of these

Subtopic:  Relative Motion |
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