Motion in a Plane

A particle moves so that its position vector is given by r = t x + t y, where is a constant. Which of the following is true?

1. Velocity is perpendicular to r and acceleration is directed towards the origin.
2. Velocity is perpendicular to r and acceleration is directed away from the origin.
3. Velocity and acceleration both are perpendicular to r
4. Velocity and acceleration both are parallel to r

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 10-4 J by the end of the second revolution after the beginning of the motion?

1. 0.18 m/s2
2. 0.2 m/s2
3. 0.1 m/s2
4. 0.15 m/s2

In the given figure, a = 15 m s-2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is [figure]

1. 4.5 m s-1
2. 5.0 m s-1
3. 5.7 m s-1
4. 6.2 m s-1

If vectors A = t i + t j and B = t2 i + t2 j are functions of time, then the value of t at which they are orthogonal to each other is

1. t =
2. t = 0
3. t = 4
4. t = 2

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