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A woman and her dog are out for a morning run to the river, which is located 4.0 $\mathrm{km}$ away. The woman runs at 2.5 $\mathrm{m} / \mathrm{s}$ in a straight line. The dog is unleashed and runs back and forth at 4.5 $\mathrm{m} / \mathrm{s}$ between his owner and the river, until the woman reaches the river. What is the total distance run by the dog?

$7.2 \times 10^{3} m$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Simon Fraser University

University of Winnipeg

McMaster University

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this problem. We know the constant speed of the woman which is 2.5 meters per second, and she's headed toward a river which is four kilometers away. We need to turn everything into the same unit. So we're gonna convert kilometers two meters knowing that there's 1000 meters in each kilometer. So our distance or displacement is 4000 meters, so that we have a dog that's traveling at a different speed for that whole time. But we need to calculate what that time is. So because distance is velocity, times time, we could rearrange that south up for tea. It would be the distance divided by the speed. The distance is 4000. That speed is 2.5 of the woman. So our time is 1600 seconds. So that whole time the dog is traveling at a constant speed of 4.5 litres per second. Now the dog is going back and forth, and so clearly would be accelerating and decelerating. But this is the average speed of the dog. So if the dog is traveling at the speed for or this average feed for that whole time period, the distance travelled by the dog would just be the velocity just 4.5 times that total time of 1600 circuits, so that would give us 7200 meters or back two kilometers, 7.2 kilometers.

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