A bar of mass m resting on a smooth horizontal plane starts moving due to a constant force F . In the process of its rectilinear motion the angle between the direction of this force and the horizontal varies as =k x , where k is a constant and x is the distance traversed by the bar from its initial position. The velocity (v) of the bar as a function of the angle is

Step-by-step solution

Component of force responsible for horizontal motion is F . So, acceleration of bar, a= F m As acceleration, a= d v d t , we have d v d t = F m we can also express this as, array ll & d v d x d x d t = F m & v d v= F m d x array Integrating both sides and putting =k x , we get v d v= F k x m d x array ll & v^2 2 = F m k x d x & v^2 2 = F m ( k x k ) & v^2= 2 F k x m k & v= 2 F m k array