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Chapter 2: Problem 187

A particle moves \(4 \mathrm{~m}\) in the south direction. Then it moves $3 \mathrm{~m}$ in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity? (A) \((5 / 7)\) (B) \((7 / 5)\) (C) \((14 / 5)\) (D) \((5 / 14)\)

Short Answer

Expert verified
The ratio between average speed and average velocity is (B) \((7 / 5)\).

Step by step solution

01

Calculate the total distance traveled

In the problem, the particle moves 4m in south direction and 3m in west direction. The total distance traveled by the particle is the sum of these distances: Total distance = 4m (south) + 3m (west) = 7m
02

Calculate the total displacement of the particle

The displacement of the particle is the shortest distance between the initial and final positions of the particle. We can treat the problem as a right-angled triangle with sides 4m and 3m. The displacement is the hypotenuse of the triangle. Using the Pythagorean theorem, we can calculate the displacement: Displacement = \(\sqrt{(4m)^2 + (3m)^2}\) = \(\sqrt{16m^2 + 9m^2}\) = \(\sqrt{25m^2}\) = 5m
03

Calculate the average speed

The average speed is calculated by dividing the total distance by the time taken. In this case, the total distance is 7m, and the time taken is 2 seconds: Average speed = Total distance / Time = 7m / 2s = 3.5 m/s
04

Calculate the average velocity

The average velocity is calculated by dividing the total displacement by the time taken. In this case, the total displacement is 5m, and the time taken is 2 seconds: Average velocity = Total displacement / Time = 5m / 2s = 2.5 m/s
05

Find the ratio between average speed and average velocity

To find the ratio between the average speed and average velocity, divide the average speed by the average velocity: Ratio = Average speed / Average velocity = 3.5 m/s / 2.5 m/s = 7/5 The answer is (B) \((7 / 5)\).

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Most popular questions from this chapter

A particle is moving in a circle of radius \(\mathrm{R}\) with constant speed. It covers an angle \(\theta\) in some time interval. Find displacement in this interval of time. (A) \(2 \mathrm{R} \cos (\theta / 2)\) (B) \(2 \operatorname{Rsin}(\theta / 2)\) (C) \(2 \mathrm{R} \cos \theta\) (D) \(2 \mathrm{R} \sin \theta\)

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