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Contents

Power

• Time rate at which work is done

The average power

$$P_{\text{av}} = \frac{\Delta w}{\Delta t}$$

• $\Delta w$ is the average quantity of work done

• $\Delta t$ is the time interval

Units of Power

$$\text{Wat} = \frac{\text{Joule}}{\text{second}}$$

Instantaneous power

$$P = \lim_{\Delta t \rightarrow 0} \frac{\Delta w}{\Delta t}$$

If forces act on a moving object, we can express the corresponding power in terms of force and velocity:

$$P_{\text{av}} = \frac{F_{\parallel} \Delta s}{\Delta t} = F_{\parallel} v_{\text{av}}$$

• $\Delta s$ is the magnitude of displacement $\Delta \vec{s}$

Int the limit we get the instantaneous work:

$$P = F_{\parallel} v$$

Adams Law Markov chain Monte Carlo (MCMC) inference