Motion in a Plane

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 )

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 s. The acceleration of the particle is

1. 15 m/s2
2. 25 m/s2
3. 36 m/s2
4. 5 m/s2

A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is

1. 40 m
2. 50 m
3. 60 m
4. 20 m

A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

1. 1 m/s2
2. 7 m/s2
3. 7 m/s2
4. 5 m/s2

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

1. 60
2. 15
3. 30
4. 45