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Chapter 2: Problem 27

Running along a rectangular track \(50 \mathrm{~m} \times 40 \mathrm{~m}\) you complete one lap in \(100 \mathrm{~s}\). What is your average velocity for the lap?

Short Answer

Expert verified
Answer: The average velocity of the runner is 0 m/s.

Step by step solution

01

Determine the track's dimensions

The given dimensions of the rectangular track are \(50 \mathrm{~m}\) and \(40 \mathrm{~m}\).
02

Calculate the total distance traveled

To find the total distance traveled, we need to find the perimeter of the rectangular track. The formula for the perimeter of a rectangle is \(P = 2 \times (L+W)\), where L is the length and W is the width. Here, the length L is \(50 \mathrm{~m}\) and the width W is \(40 \mathrm{~m}\). So, the perimeter or total distance is: \(P = 2 \times (50 + 40) = 2 \times 90 = 180 \mathrm{~m}\)
03

Determine the time taken to complete one lap

The given time taken to complete one lap is \(100 \mathrm{~s}\).
04

Find the displacement after completing one lap

Since the runner starts and ends at the same point after completing one lap, the total displacement is \(0 \mathrm{~m}\).
05

Calculate the average velocity

The formula for average velocity is: \(Average \ Velocity = \cfrac{Total \ Displacement}{Total \ Time}\) As the displacement is \(0 \mathrm{~m}\), the average velocity is: \(Average \ Velocity = \cfrac{0 \mathrm{~m}}{100 \mathrm{~s}} = 0 \cfrac{\mathrm{m}}{\mathrm{s}}\) Hence, the average velocity for the lap is \(0 \cfrac{\mathrm{m}}{\mathrm{s}}\).

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Most popular questions from this chapter

An object is thrown vertically and has an upward velocity of \(25 \mathrm{~m} / \mathrm{s}\) when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?

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