The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) $$v \propto {1 \over {\sqrt x }}$$. Find how the magnitude of the force (F) on the particle depends on x?

A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is time and k = 1 Ns^$$-$$1. The distance the block will travel in 6 seconds is

A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 ms^$$-$$2. (ii) lowered with an acceleration of 4.9 ms^$$-$$2. The ratio of tension in the first and second case is