When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60^o with horizontal, it can travel a distance x₁ along the plane. But when the inclination is decreased to 30^o and the same object is shot with the same velocity, it can travel x₂ distance. Then x₁ : x₂ will be :

The x and y coordinates of the particle at any time are x = 5t $$-$$ 2t² and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is

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

A particle moves so that its position vector is given by $$\overrightarrow r = \cos \omega t\,\widehat x + \sin \,\omega t\,\widehat y,$$ where $$\omega $$ is a constant.

Which of the following is true?