The direction of motion of the 100-g cart is to the right.
The 100-g cart will continue to move to the right after the string is burned through. This is because of the conservation of momentum.
When the carts are connected by the spring, they are considered as a single system. The spring is compressed, storing potential energy. When the string is burned and the carts are separated, this potential energy is converted into kinetic energy.
Since the carts were originally moving to the right at 1.0 m/s, the 100-g cart will continue to move in the same direction with the same velocity. The momentum of the cart is conserved.
Complete question :-
The air-track carts in the figure(Figure 1) are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 130 N/m and is compressed 4.4cm . The carts slide past a flame that burns through the string holding them together. a.) What is the speed of 100- cart? b.) What is the direction of the motion of 100- cart?(right or left) c.)What is the speed of 300- cart? d. What is the direction of the motion of 300- cart? (right or left)