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Chapter 2: Problem 7

A cyclist travels \(10.0 \mathrm{km}\) east in a time of $11 \mathrm{min} 40 \mathrm{s}$ What is his average velocity in meters per second?

Short Answer

Expert verified
Answer: The cyclist's average velocity is approximately 14.29 meters per second.

Step by step solution

01

Identify the given information

The distance traveled by the cyclist is 10.0 km and the time taken is 11 minutes and 40 seconds.
02

Convert distance to meters

Since 1 km equals 1,000 meters, we can find the distance in meters by multiplying the given distance in kilometers by 1,000: Distance = 10.0 km * 1,000 = 10,000 meters
03

Convert time to seconds

First, we need to convert the minutes to seconds and then add them to the given seconds. Since 1 minute equals 60 seconds, we can convert 11 minutes to seconds by multiplying: Time in seconds = 11 minutes * 60 = 660 seconds Now, add the given 40 seconds to the time in seconds: Total time in seconds = 660 + 40 = 700 seconds
04

Calculate average velocity

Now we have the distance in meters and the time in seconds, and we can find the average velocity using the formula: Average velocity = Distance / Time Average velocity = 10,000 meters / 700 seconds
05

Solve for average velocity

Divide 10,000 meters by 700 seconds to get the average velocity: Average velocity = 14.29 meters/second (rounded to two decimal places) The cyclist's average velocity is approximately 14.29 meters per second.

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Most popular questions from this chapter

Two cars, a Toyota Yaris and a Jeep, are traveling in the same direction, although the Yaris is \(186 \mathrm{m}\) behind the Jeep. The speed of the Yaris is \(24.4 \mathrm{m} / \mathrm{s}\) and the speed of the Jeep is $18.6 \mathrm{m} / \mathrm{s}$. How much time does it take for the Yaris to catch the Jeep? [Hint: What must be true about the displacement of the two cars when they meet?]
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In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. A streetcar named Desire travels between two stations \(0.60 \mathrm{km}\) apart. Leaving the first station, it accelerates for \(10.0 \mathrm{s}\) at $1.0 \mathrm{m} / \mathrm{s}^{2}$ and then travels at a constant speed until it is near the second station, when it brakes at \(2.0 \mathrm{m} / \mathrm{s}^{2}\) in order to stop at the station. How long did this trip take? [Hint: What's the average velocity?]
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