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 :

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h₁ and h₂. Which of the following is correct ?

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x² . If it were launched at an angle $$\theta $$₀ with speed v₀ then (g = 10 ms^–2) :