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# Displacement, Velocity, Acceleration

How fast are you moving? How fast is how fast you are moving changing? Displacement, velocity, and acceleration form the art of understanding movement, Calculus-style.

# Average Velocity

Point $$P$$ departs from the origin $$(0,0)$$ at time $$t=0$$ and travels in a straight line to $$(3t, 4t)$$ at time $$t$$. What is the average speed of $$P?$$

A car travels from city $$A$$ to city $$B$$ with a speed of $$19 \text{ miles/h}$$ and back from city $$B$$ to city $$A$$ with a speed of $$3 \text{ miles/h}.$$ What is the average speed of the car (in miles/h) during this round trip?

A car leaves point $$A$$ at $$8 \text{am}$$ and arrives at point $$B$$ at $$3 \text{pm}$$ on the same day. If the car travels a total distance of $$623$$ miles, then what is its average speed (in miles/hour)?

The diagram below shows a detour (first $$8\text{ m}$$ north, then $$18\text{ m}$$ southeast) from a starting point to an end point. The diagram also shows the shortest distance $$12 \text{ m}$$ between the starting and end points.

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If a person takes the detour and reaches the end point in $$23$$ seconds, what is the average velocity of the person?

A runner completes a $$126$$ meter lap in $$13$$ seconds. What is average speed of the runner during this lap (in meters/second)?

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