### Vehicular Signal Acquisition and Processing - Week 10

**Discussion on an Alternate Approximation of the Vehicle's Power Output**

The previous method for calculating the Power Output was by approximating the force that acted on the mass of the vehicle, determining the work done by this force being exerted over a distance, and finally determining the power output by determining the rate at which the work was done.

An alternate method looks at the Kinetic Energy of the vehicle. The Kinetic Energy of an object is also expressed in Joules (kg*m^{2}/s^{2}). The formula used to determine the Kinetic Energy of an object is:

*Kinetic Energy = 1/2 * Mass * Velocity*^{2}

Additional background material on Kinetic Energy, what it is, and how it differs from Potential Energy, can be found here. A good explanation as to why this formula explains the Kinetic Energy of an object here.

For the purposes of the project, it doesn't help much to know the instantaneous Kinetic Energy of the object at any given point. However, if we examine the derivative of Kinetic Energy, dKE/dt, we can determine the rate of change in Kinetic Energy - essentially the work done on the object within a given region of time. Knowing the work done, and the duration of time it was done in, gives the power output.

*Work = dKE/dt*

PowerOutput=Work/t

To determine an approximation for dKE/dt, a similar approach to determining the acceleration the previous weeks will be used: interpolate a velocity a duration back from the current time (for example, one second), and use the two velocity values in the discrete approximation of the derivative. The discrete approximation is:

*dKE/dt = (KE*_{now} - KE_{now-duration})/(duration)