Speed is a scalar quantity. This means that its value stands on its own without a direction. Something similar to speed is velocity. Velocity has the same number as speed, but also includes a direction. For example, I might be driving at a speed of 60 miles per hour, whereas my velocity is 60 miles per hour, west. This type of quantity-one that includes a direction-is called a vector quantity. Acceleration, like velocity, is a vector quantity. If I continue driving at the same speed but I follow a curve in the road that changes my direction, I might then be driving 60 miles per hour, north. Since my speed remained 60 miles per hour, the number corresponding to my acceleration was zero before and is zero after. However, the change in direction means that acceleration has changed.
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This can be achieved in many different ways; one that is easy to visualize is an object moving in a circle, at a constant speed. In this case:* The velocity constantly changes, since the direction changes.
* The acceleration constantly changes, since the acceleration vector points towards the center of the circle - so this direction changes as well.
When an object changes its direction of motion but not its speed: for example the tip of a clock hand as is marks out time, or a car going at constant speed around a curve.