State the similarities and differences between the following pairs of terms: distance and displacement, speed and velocity.

Distance and displacement are both measures of how far something has travelled. However, they measure travel in different ways. Specifically, distance measures the total length of the path traveled. Displacement, as its name suggests, measures how far out of place the object ends.
So, if an object travels four meters north, and then three meters south, it has travelled a distance of seven meters. However, the object's displacement, the space between it and its origin point, is not seven meters, because it travelled back on itself. The object went forward by four and backward by three, so it ends up one meter displaced from its start.
Speed and velocity differ in a similar way. Both measure rate of travel over time. However, speed is a scalar measure of the distance covered over a given time. Velocity, by contrast, measures the displacement in a certain direction over a given time. For example, the moon orbits around the Earth at a speed of a little more than 3,500 kilometers per hour. However, relative to the Earth, the moon's long-term velocity is zero! Because its elliptical orbit is constant and it always returns to the same position, it never displaces from its starting point. For all its speed, it undoes its own progress every month.
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