Starting from the origin at time t = 0, with initial velocity 5$$\widehat j$$ ms^-1 , a particle moves in the x-y plane with a constant acceleration of $$\left( {10\widehat i + 4\widehat j} \right)$$ ms^-2. At time t, its coordinates are (20 m, y₀ m). The values of t and y₀ are, respectively:

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms^–1) of this person as observed from train B will be close to :
(take the distance between the tracks as negligible)

A particle starts from the origin at t = 0 with an
initial velocity of 3.0 $$\widehat i$$ m/s and moves in the
x-y plane with a constant acceleration $$\left( {6\widehat i + 4\widehat j} \right)$$ m/s² . The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is :-

A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\omega $$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow v \left( t \right)$$ and acceleration $$\overrightarrow a \left( t \right)$$ of the particle :