   Chapter 2, Problem 3P

Chapter
Section
Textbook Problem

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.

(a)

To determine
The average velocity of the car.

Explanation

Given info: The speed of the car between the first pair of cities is 80.0km/h and the time taken to cover the first pair of cities is 30.0min .

Explanation:

The formula to calculate the distance is,

Δx1=v1(Δt1)

Here,

Δx1 is the distance covered by the car in the first pair of cities.

v1 is the speed of the car between the first pair of cities.

Δt1 is the time taken to cover the first pair of cities.

Substitute 80.0km/h for v1 and 30.0min for Δt1 to find Δx1 .

Δx1=(80.0km/h)((30.0min)(1.00h60.0m))=40.0km

Thus, the distance of the car during first pair of cities is 40.0km

The formula to calculate the distance is,

Δx2=v2(Δt2)

Here,

Δx2 is the distance covered by the car in the second pair of cities.

v2 is the speed of the car between the second pair of cities.

Δt2 is the time taken to cover the second pair of cities.

Substitute 100.0km/h for v2 and 12.0min for Δt2 to find Δx2 .

Δx2=(100.0km/h)((12.0min)(1.00h60.0m))=20.0km

Thus, the distance of the car during the second pair of cities is 20.0km .

Formula to calculate the distance is,

Δx3=v3(Δt3)

Here,

Δx3 is the distance covered by the car in the third pair of cities

v3 is the speed of the car between the third pair of cities.

Δt3 is the time taken to cover the third pair of cities.

Substitute 40.0km/h for v3 and 45.0min for Δt3 to find Δx3 .

Δx3=(40.0km/h)((15.0min)(1.00h60.0m))=30.0km

Thus, the distance of the car during the third pair of cities is 30

(b)

To determine
The distance between the initial and final cities.

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