Question

a particle of mass m is given velocity $V_{0}$ on rough horizontal surface

Coefficient of friction is $\mu$

there is also variable external force acts on particle given by F=kV where K is constant & V is instaneous velocity

direction of force at any instant is perpendicular to velocity

the particle moves in an instaneous circular path of variable radius

then time taken by particle to stop is $V_{c}/\mu g$

time taken to reduce the angle between acceleration and velocity from $60^{0}$ to $30^{0}$ is $2m/\sqrt{3k}$

Total distance covered is $V_{0}^2/2\mu g$

the radius of curvature of path at any time is $m/k(v-\mu gt/2)$

Answer 1