Question: is watt per second a unit of power

Answer: Yes, The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis it is described by M L 2 T − 3 (\displaystyle (\mathsf (ML))^(2)(\mathsf (T))^(-3)) .