Question

A particle moves along a space curve,r=r(t) is the time measured from some initial time. if v=/dr/dt/=ds/dt is the magnitude of the velocity of the particle (s is the arc length along space curve measured from the initial position),prove that the acceleration a of particle is given by a=dv/dtT+v^2/pN where T and N are unit tangent and normal vectors to the space curve and      p=|d^2r/ds^2|^-1={(d^2/ds^2)^2+.     (d^2y/ds^2)^2 + (d^2z/ds^2)^2}^-1/2

Answer 1