Answered: A person travels by car from one city…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter3: Motion Along A Straight Line

Section: Chapter Questions

Problem 26P: The Shanghai maglev train connects Longyang Road to Pudong International Airport, a distance of 30...

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Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas.

(a) Determine the average speed for the trip.

(b) Determine the distance between the initial and final cities along the route.

Expert Solution

Step 1

AVERAGE SPEED :

$v_{a v} = \frac{d_{1} + d_{2} + d_{3}}{t_{1} + t_{2} + t_{3} + t_{4}}$

Given:

Speed :

$v_{1} = 80 k m / h v_{2} = 100 k m / h v_{3} = 40 k m / h$

Time :

$t_{1} = 30 m i n = \frac{30}{60} h = 0.5 h t_{2} = 12 m i n = \frac{12}{60} h = 0.2 h t_{3} = 45 m i n = \frac{45}{60} h = 0.75 h t_{4} = 15 m i n = \frac{15}{60} h = 0.25 h$

Distance is calculated by product of speed and time during this interval .

$d = v \times t$

By plugging given values we get

$d_{1} = 80 \times 0.5 = 40 k m$

$d_{2} = 100 \times 0.2 = 20 k m$

$d_{3} = 40 \times 0.75 = 30 k m$

Therefore average speed is calculated by subsituting value of d and t in formula we get

$v_{a v} = \frac{40 + 20 + 30}{0.5 + 0.2 + 0.75 + 0.25} = \frac{90}{1.7} = 52.9 k m h^{- 1}$

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