A bar of mass m resting on a smooth horizontal plane starts moving due to the force `F=mg//3` of constant magnitude. In the process of its rectilinear motion the angle `alpha` between the direction of this force and the horizontal varies as `alpha=as`, where a is a constant, and s is the distance traversed by the bar from its initial position. Find the velocity of the bar as a function of the angle `alpha`.

A small bar starts sliding down an inclined plane forming an angle alpha with the horizontal. The friction coefficient depends on the distance x covered as k=ax , where a is a constant. Find the distance covered by the bar till it stops, and its maximum velocity over this distance.

A point moves along an arc of a circle of radius R. Its velocity depends on the distance covered s as v=asqrts , where a is a constant. Find the angle alpha between the vector of the total acceleration and the vector of velocity as a function of s.

A bar of mass m resting on a smooth horizontal plane starts moving due to force |F| =(mg)/9 . The magnitude of force remains constant with time. The force vector makes an angle theta with the horizontal which varies with the distance covered as theta =Cx . if the constant , C=10 (("degree")/("meter")) , then the speed of the bar , when theta becomes equal to 30^@ for the first time is, (Take , g =10 m//s^2 )

A point moves along an arc of a circle of radius R. Its velocity depends on the distance covered s as v=sqrts , where a is a constant. Find the angle alpha between the vector of the total acceleration and the vector of velocity as a function of s.

A locomotive of mass m starts moving so that its velocity varies according to the law V=alphasqrts, where alpha is a constant and s is the distance covered. Find the total work done by all the forces acting on the locomotive during the first t seconds after the beginning of motion.

A locomotive of mass 'm' starts moving so that its velocity varies as v=alpha s^(2/3) where alpha is a positive constant and 's' is the distance travelled .The total work done by all the forces acting on the locomotive during first 't' second after the start of motion is