In this study, we propose a control strategy for a power-assisted cart based on its motion state. The power-assisted cart we developed has one motor, a differential gear, and brakes. This cart uses the motor and the differential gear for moving forward, and applying brakes to either wheel allows the cart to turn both left and right. Therefore, the power-assisted cart can support the user when going straight and turning despite having only one motor. In the past we developed a control method that allows to control the cart's speed around the operation point in order to keep its magnitude constant when the cart starts turning. This was necessary, as the differential gear causes a speed change during turning, because of its characteristics. However, the desired behavior when transitioning from straight motion to turning motion is different to the desired behavior when going from turning motion to straight motion. Therefore, in this paper we propose a control method to adjust the speed in the direction of motion based on the state of the cart. We validated the effectiveness of the proposed method through experiments and discussed the results.