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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.

Imgur

Imgur

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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