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 x1 at time t1 to position x2 at time t2, then the displacement is x2-x1 (which can be positive or negative, depending on whether x2 is to the right or left of x1) and the average velocity :

vave=(x2-x1)/(t2-t1)=Deltax/Deltat
Due to the effect of direction changes, there is no simple relationship between average speed and average velocity over a general path. However, we can find a relationship when we look at the instantaneous quantities.