A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu$$_k. then, the block's acceleration 'a' is given by :

(g is acceleration due to gravity)

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

A particle is projected with velocity v₀ along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = $$-$$ $$\alpha$$x². The distance at which the particle stops :

A particle moving in the xy plane experiences a velocity dependent force
$$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$$ , where v_x and v_y are the
x and y components of its velocity $$\overrightarrow v $$ . If $$\overrightarrow a $$ is the
acceleration of the particle, then
which of the following statements is true for the particle?