Motion in a Plane

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

A particle moves in x-y plane according to rule x = a t and y = a t. The particle follows

1. an elliptical path
2. a circular path
3. a parabolic path
4. a straight line path inclined equally to x and y-axes

A particle has initial velocity (3 i + 4 j) and has acceleration (0.4 i + 0.3 j). Its speed after 10 s is

1. 7 units
2. 7 2 units
3. 8.5 units
4. 10 units

Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? [figure]

1. b + c = f
2. d + c = f
3. d + e = f
4. b + e = f

A particle of mass m is projected with velocity v making an angle of 45 with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

1. mv 2
2. zero
3. 2mv
4. mv/ 2

A and B are two vectors and θ is the angle between them. If | A B| = 3 ( A B), the value of θ is

1. 45
2. 30
3. 90
4. 60

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ( 3, 3 ). The path of the particle makes with the x-axis an angle of

1. 45
2. 60
3. 0
4. 30