A truck driver has a shipment of apples to deliver to a...

Name: Problem 53, Chapter 2: College Physics: A Strategic Approach
Uploaded: 2020-11-01T15:17:50-08:00
Duration: 4 min 16 s
Channel: Guilherme Barros
Description: A truck driver has a shipment of apples to deliver to a destination 440 miles away. The trip usually takes him 8 hours. Today he finds himself daydreaming and realizes 120 miles into his trip that he is running 15 minutes later than his usual pace at this point. At what speed must he drive for the remainder of the trip to complete the trip in the usual amount of time?

A truck driver has a shipment of apples to deliver to a destination 440 miles away. The trip usually takes him 8 hours. Today he finds himself daydreaming and realizes 120 miles into his trip that he is running 15 minutes later than his usual pace at this point. At what speed must he drive for the remainder of the trip to complete the trip in the usual amount of time?

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Key Concepts

Uniform Motion Principle

This key concept refers to the relationship between distance, speed, and time, typically summarized by the equation distance = speed × time. It is fundamental to understanding and solving problems where objects move at a constant rate.

Segmented Motion Analysis

This concept involves breaking a journey into different parts or segments and analyzing each portion individually. It is particularly useful in problems where different segments of a trip have different speeds or time constraints, which affects the overall outcome.

Time Adjustment and Compensation

This key idea focuses on managing and compensating for time deviations within a journey. When a delay occurs in one segment, adjustments in speed or timing in the remaining segments are required to meet an overall time goal.

Unit Conversion

Accurate problem solving in motion problems often depends on consistent units. Converting units, such as minutes to hours, ensures that calculations using formulas like distance = speed × time are correct and consistent.

Transcript

00:01 In this problem, we're going to talk about uniform motion.

00:03 And what we need to remember is that the velocity is defined as the variation in position, delta x, divided by the variation in time, delta t.

00:13 And we have a truck driver that has to drive 440 miles in a time of 8 hours.

00:27 So first, let's calculate what velocity this amounts to.

00:32 This is equal to 440 miles divided by 8 hours.

00:39 So this is equal to 55 miles per hour.

00:47 And after the truck driver drove 120 miles, he realizes that he is 15 minutes late with respect to the position where he should be, with respect to the time that should have passed, in 120 miles if he were to complete his trajectory in 8 hours.

01:19 So he wants to compensate to make up for this lost time by increasing his speed.

01:27 And we want to find what is this new speed, v -prime.

01:34 So first, i'm going to calculate how long it should take for the truck driver to drive 120 miles if he were driving at a speed of 55 miles per hour.

01:52 So the time, delta t prime is equal to delta x prime, divided by v, delta x prime is 120 hours, well, i'm sorry, 120 miles, divided by 55 miles per hour.

02:07 So delta t prime is equal to 2 .18 hours.

02:13 Okay? now, 0 .18 hours is equal to 11 minutes.

02:18 All we have to do is multiply 0 .18 by 60...

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