Looking more closely, however, we see that this calculation actually gives the average speed of the object over the interval of time . For instance, if it takes us 2.5 hours to drive a distance of 200 miles to Boston, then we have averaged miles per hour. However, we may have been going only 65 miles per hour when we went through a speed trap, and 90 mph at other times. The average speed over an interval of time may have very little resemblance to the speed at a particular instant of time, i.e., to the instantaneous speed. For an object in motion, it is the instantaneous velocity that gives the best description of its progress.
Velocity differs from speed in that it has both a magnitude and a direction.
If the object moves to the right on the -axis, we give its velocity a positive value, and negative if it moves to the left. The answer will be related to the solution of the other problem we have introduced. The Tangent Line problem is not trivial, although for some shapes and points we already know how to solve it. For example, for any point on the circumference of a circle, we need only construct the line perpendicular to the radius drawn to the point. The answers are not so clear.