1. A sheet transport apparatus, comprising: a first motor and a second motor; a first roller configured to: rotate upon receiving motive power from the first motor; and transport a sheet in a predetermined transport direction; a second roller which is provided on a downstream side of the first roller in the transport direction and which is configured to: rotate upon receiving motive power from the second motor while nipping the sheet transported by the first roller at a nip position; and transport the sheet further downstream in the transport direction; and a controller, wherein the controller includes: a motor control unit configured to perform a first process in which the first motor is controlled to rotate the first roller and a second process in which the second motor is controlled to rotate the second roller; and a first reaction-force estimating observer configured to calculate a first estimated value which is an estimated value of a reaction force acting on the first motor, based on control input for the first motor and control output corresponding to the control input, the motor control unit is configured to: start the second process before the sheet transported in the first process arrives at the nip position; determine a rotation amount of the second roller during a period from a reaction-force change point at which a predetermined change has occurred in the first estimated value until the second roller stops, on condition that the predetermined change has occurred in the first estimated value, the predetermined change indicating that the sheet has been started to be transported upon receiving action of force from the second roller; and arrange the sheet at a target position positioned on a downstream side of the nip position in the transport direction by controlling the second motor in the second process, so that the second roller rotates by the rotation amount determined by the motor control unit during the period from the reaction-force change point until the second roller stops.