Motion in a Plane

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

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

1. 10 m/s, 0
2. 0, 0
3. 0, 10 m/s
4. 10 m/s, 10 m/s.

For angles of projection of a projectile at angle (45 - ) and (45 + ), the horizontal range described by the projectile are in the ratio of

1. 2 : 1
2. 1 : 1
3. 2 : 3
4. 1 : 2.

The vectors A and B are such that | A + B| = | A - B|. The angle between the two vectors is

1. 45
2. 90
3. 60
4. 75

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is

1. a v2 + v12
2. av + v1
3. av - v1
4. a2v2 - v12