A particle moves so that its position vector is given by Where ω is a constant.
Which of the following is true?

A projectile is fired from the surface of the earth with a velocity of with the horizontal. Another projectile fired from another planet with a velocity of 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 is

The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos(ωt)
Where X = displacement at time t
ω = frequency of oscillation
Which one of the following graphs shows correctly the variation 'a' with 't' ?

A bullet is fired from a gun at the speed if in the direction 30°  above the horizontal . The maximum height attained by the bullet is

A particle moves so that its position vector is given by Where ω is a constant.
Which of the following is true?

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. I this particle were projected with the same speed at an angle ‘θ’ to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by:

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by :

The x and y coordinates of the particle at any time are x = 5t – 2t^² and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is

The position vector of a particle as a function of time is given by:

Where R is in meters, t is in seconds and and denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Two particles A and B move with constant velocities and At the initial moment their position vectors respectively. The condition for particles A and B for their collision is:

A projectile is fired from the surface of the earth with a velocity of with the horizontal. Another projectile fired from another planet with a velocity of 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 is