## Speed and Velocity

Average speed is typically defined by distance traveled/time taken. This is not a useful quantity, as it has no notion of direction. For example, in two dimensions, we could have a particle travel at an average speed of 1 cm/second for 10 seconds, but then we wont know where the particle is at the end of the 10 seconds.Instead of speed, physicists use velocity:

**Average velocity = displacement**/time

Displacement is defined as the distance between the final position and the initial position, keeping the sense of direction between them. In 1D, if a particle moves from position x_{1} at time t_{1} to position x_{2} at time t_{2}, then the displacement is x_{2}-x_{1} (which can be positive or negative, depending on whether x2 is to the right or left of x1) and the average velocity :

- v

_{ave}=(x

_{2}-x

_{1})/(t

_{2}-t

_{1})=Deltax/Deltat

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