Motion in a Plane

The position vector of a particle R as a function of time is given by R = 4 (2 t) i + 4 (2 t) j. Where R is in meters, t is in seconds and i and j denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

1. Magnitude of the velocity of particle is 8 meter/second.
2. Path of the particle is a circle of radius 4 meter.
3. Acceleration vector is along - R.
4. Magnitude of acceleration vector is v2R where v is the velocity of particle.

Two particles A and B, move with constant velocities v1 and v2. At the initial moment their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is

1. r1 v1 = r2 v2
2. r1 - r2 = v1 - v2
3. r1 - r2| r1 - r2| = v2 - v1| v2 - v1|
4. r1 v1 = r2 v2

A ship A is moving Westwards with a speed of 10 km h-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1. The time after which the distance between them becomes shortest, is

1. 5 2 h
2. 10 2 h
3. 0 h
4. 5 h

A projectile is fired from the surface of the earth with a velocity of 5 m s-1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m s-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m s-2) is (Given g = 9.8 m s-2)

1. 3.5
2. 5.9
3. 16.3
4. 110.8

A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector ( vav) from t = 0 to t = 5 s is

1. 15 (13 i + 14 j )
2. 73 ( i + j )
3. 2 ( i + j )
4. 115 ( i + j )

The velocity of a projectile at the initial point A is (2 i + 3 j) m/s. Its velocity (in m/s) at point B is [figure]

1. 2 i - 3 j
2. 2 i + 3 j
3. -2 i - 3 j
4. -2 i + 3 j

Vectors A, B and C are such that A B = 0 and A C = 0. Then the vector parallel to A is

1. A B
2. B + C
3. B C
4. B and C

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

1. = -1 ( 14 )
2. = -1(4)
3. = -1(2)
4. = 45

A particle has initial velocity (2 i + 3 j ) and acceleration (0.3 i + 0.2 j ). The magnitude of velocity after 10 seconds will be

1. 9 2 units
2. 5 2 units
3. 5 units
4. 9 units

A projectile is fired at an angle of 45 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

1. 45
2. 60
3. -1 ( 12 )
4. -1 ( 32 )