A particle is sliding along a smooth radial grove in a circular turntable which is rotating with constant angular speed Ω. The distance of the particle from the rotation axis at time t is
observed to be
r = b cosh Ωt
for t ≥ 0, where b is a positive constant. Find the speed of the particle (relative to a fixed reference frame) at time t, and find the magnitude and direction of the acceleration.