Most of the equations that we have been using in this chapter are used in the context of an average velocity, because they are evaluated as an average between two endpoints. In more complicated cases, however, such as the trip from Wilmington to Washington, the average velocity was quite different from the multiple values of instantaneous velocity as the car traveled, stopped, moved again, and then turned around. What was the correct velocity to describe that motion? The answer is that both values given were correct: the average speed was 80 km/h while the instantaneous speed was 100 km/h while driving on the highway.
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In order to answer that question, we must distinguish between average and instantaneous velocities. The 
Now imagine that the car was driving in bumper-to-bumper traffic—speeding up and slowing down. The position-time graph for this motion might be similar to the figure on the right. The 
In real-world cases, the instantaneous velocity might not vary suddenly (as in the previous example), but smoothly. After all, you don't usually slam on the brakes suddenly! The instantaneous velocity is the tangent to the curve in a position-time graph, as is shown in the figure at right. When the tangent to the curve has a shallow slope, the instantaneous velocity is small. When the tangent to the curve has a steep slope, the instantaneous velocity is large. Can you find a location on the graph where the instantaneous velocity is negative? 
