The formula for instantaneous power when given velocity and force is P = F * v, where P represents power, F is force, and v is velocity. Instantaneous power can also be derived by differentiating work done with respect to time. In general, power is defined as the work done divided by the time taken, expressed as P = W/t. Thus, when considering instantaneous conditions, power can be calculated as force multiplied by the instantaneous velocity. Understanding these formulas is crucial for analyzing the dynamics of moving objects.