A particle starting from the point (1, 2) moves in a straight line in the XY plane. Its coordinates at a later time are (2, 3). The path of the particle makes, with the x-axis, an angle of

1. 30° 

2. 45°

3. 60° 

4. data insufficient

Subtopic:  Position & Displacement |
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A particle is projected from a horizontal plane (x-z plane) such that its velocity vector at time t is given by v=ai^+b-ctj^. Its range on this horizontal plane is given by 

1. bac

2. 2bac

3. 3bac

4. None 

Subtopic:  Projectile Motion |
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A man is walking on the road with a speed 3 m/s. Rain is falling vertically at speed 3 m/s. At what angle from
the vertical, man has to hold his umbrella to avoid the rain drops?
1. 45o 

2. 30o

3. 60o 

4. 90o

Subtopic:  Relative Motion |
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A river is 1 km wide. The banks are straight and parallel. The current is 5 km/h and is parallel to the banks. A boat has a maximum speed of 3 km/h in still water. In what direction should the boat head so as to arrive at point B directly opposite to its starting point A?

1. directly across the river

2. head 53° upstream from the line AB

3. head 37° upstream from the line AB

4. the trip from A to B is not possible with this speed

Subtopic:  Relative Motion |
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Two particles A and B, move with constant velocities \(\vec{v_1}\)   and  \(\vec{v_2}\) . At the initial moment their position vector are  \(\vec{r_1}\) and  \(\vec{r_2}\)  respectively. The condition for particles A and B for their collision to happen will be

1.  r1 .v1 =r2 .v2

2.  r1 x v1 =r2 x v2

3.  r1- r2 =v1- v2

4.  r1- r2r1- r2= v2- v1v2- v1

Subtopic:  Speed & Velocity |
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A particle moves along a parabolic path y = 9x2 in such a way that the x component of the velocity remains constant and has a value of 13 ms-1. It can be deduced that the acceleration of the particle will be

1. 13 j^ ms-2

2. 3 j^ ms-2

3. 23 j^ ms-2

4. 2 j^ ms-2

Subtopic:  Acceleration |
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Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are v1,v2 and v3 respectively, then:
           

1. v1>v2>v3

2. v3>v2=v1

3. v1=v2=v3

4. v1<v2<v3

Subtopic:  Projectile Motion |
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Figure below shows a body of mass M moving with a uniform speed v on a circular path of radius, R. What is the change in acceleration in going from P1 to P2
              

1. zero

2. v2/2R

3. 2v2/R

4. v2R×2

Subtopic:  Circular Motion |
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A particle is projected with a speed u at an angle θ to the horizontal. Radius of curvature at highest point of its trajectory is

1. u2cos2θ2g

2. 3u2cos2θ2g

3. u2cos2θg

4. 3u2cos2θg

Subtopic:  Circular Motion |
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii rA and rB with speeds vA and vB respectively. Their time periods of rotation are the same. The ratio of angular speed of A  to that of B will be:

1. 1: 1

2. rA : rB

3. vA : vB

4. rB : rA

Subtopic:  Circular Motion |
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