You and a friend decide to drive to New York from College...

You and a friend decide to drive to New York from College Park, Maryland (near Washington, D.C.) on Saturday over the Thanksgiving break to go to a concert with some friends who live there. You figure you have to reach the vicinity of the city at 5 P.M. in order to meet your friends in time for dinner before the concert. It's about $220 \mathrm{mi}$ from the entrance to Route 95 to the vicinity of New York City. You would like to get on the highway about noon and stop for a bite to eat along the way. What does your average velocity have to be? If you keep an approximately constant speed (not a realistic assumption!), what should your speedometer read while you are driving?

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Key Concepts

Average Velocity

Average velocity is a measure of the total displacement divided by the total time taken for that displacement. It provides an overall description of the speed and direction of motion over an interval, and in simple cases (with motion in a straight line) it can be calculated by dividing the total distance by the total time, even if the speed is not constant throughout the journey.

Constant Speed and Uniform Motion

When an object travels at a constant speed, it means that at every moment the instantaneous speed is the same as the average speed over the journey. This idealization simplifies calculations by allowing one to assume that the speedometer reading remains steady throughout the trip, equating the average velocity with the constant speed required to cover the distance in the allotted time.

Time, Distance, and Speed Relationship

The relationship between time, distance, and speed is given by the formula distance = speed × time. This fundamental equation is essential for planning and analyzing motion, as it allows one to determine the required speed to travel a certain distance in a given time or, conversely, the distance that can be covered at a specified speed over a set period.

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