The worktable of a positioning system is driven by a ball screw whose pitch $=10\mathrm{.}0$

mm $.$ The screw is connected to the output shaft of a stepper motor through a gearbox

whose ratio is $8$:$1($eight turns of the motor to one turn of the screw$).$ The stepper motor

has $28$ step angles. The table must move $475$ mm from its present position at a linear

velocity $=575m\frac{m}{m}in.$ Determine $($a$)$ how many pulses are required to move the table

the specified distance and $($b$)$ the required motor speed and pulse rate to achieve the

desired table velocity.