An archer pulls back the string of a bow to release an arrow at the target which kind of potential energy is transformed to cause the motion of the arrow?

elastic potential energy
Explanation:
The form of energy stored in the string of the bow is elastic potential energy. Elastic potential energy is the energy stored in an elastic object (such as the string of a bow) when the object is compressed/stretched by a certain amount x with respect to its natural length. The elastic potential energy stored in the object is given by
U=\frac{1}{2}kx^2U=21kx2
where k is the spring constant of the elastic string, and x is the compression/stretching.