/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 A truck driver has a shipment of... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 57

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?

Short Answer

Expert verified
The driver must drive at approximately 57.45 miles per hour for the remainder of the trip to complete it in the usual amount of time.

Step by step solution

01

Calculate normal speed

Normally, the total distance of 440 miles is covered in 8 hours. So, the normal speed is calculated by dividing total distance by total time which gives \( \frac{440 miles}{8 hours} = 55 miles/hour \)
02

Calculate time spent daydreaming

The driver has covered 120 miles at a pace 15 minutes slower than usual. Normally, 120 miles would have taken \( \frac{120 miles}{55 miles/hour} = 2.18 hours \) approximately. However, due to daydreaming, it took him 15 minutes more, that is \( 2.18 hours + \frac{15 minutes}{60} = 2.43 hours \) approximately.
03

Calculate remaining time and distance

Subtracting the time spent daydreaming from the total usual time gives the remaining time. \( 8 hours - 2.43 hours = 5.57 hours \) approximately. The remaining distance is found by subtracting the distance covered from the total distance, giving \( 440 miles - 120 miles = 320 miles \).
04

Calculate required speed for the remaining trip

To complete the remaining trip in 5.57 hours, the speed must be \( \frac{320 miles}{5.57 hours} = 57.45 miles/hour \) approximately. This is the speed the driver must maintain to complete the trip in the usual total time.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed and Distance
Understanding speed and distance is crucial in physics problems that involve motion. Speed is simply defined as the distance traveled per unit of time. It's the measure of how fast an object is moving. To calculate speed, you divide the distance by the time taken to travel that distance. Always remember the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]In our truck driver example:
  • The total distance is 440 miles.

  • The usual travel time is 8 hours.

  • To find the normal speed, use the formula to divide 440 miles by 8 hours, resulting in 55 miles per hour.
This straightforward calculation helps determine how quickly the driver is traveling under usual conditions. When you solve problems, always ensure units match and make the calculation simpler by organizing known values clearly.
Time Calculations
Understanding how to manipulate and calculate time is essential in physics. It goes beyond simply understanding what the clock says; rather, it involves calculations based on time intervals, as in our scenario. In the truck driver scenario, the driver realized he was 15 minutes behind schedule after covering 120 miles. Normally:
  • 120 miles at a speed of 55 mph should have taken approximately 2.18 hours, calculated by dividing 120 miles by 55 mph.

  • Because of the daydreaming, it took him an extra 15 minutes, so the real time spent was 2.43 hours, which is 2.18 hours plus 0.25 hours (15 minutes).
Always convert time units for consistency when doing calculations: 15 minutes becomes 0.25 hours in this case. Accurate time conversion and subtraction allow for solving how much time remains for the rest of a journey. Such calculations ensure accurate estimations for adjustments and planning.
Problem Solving in Physics
Problem solving in physics is a structured process of analyzing a scenario, applying known scientific principles, and using correct formulas to find a solution. To solve the problem effectively, break it down into smaller, more manageable steps. Let's take another look at our example, In this exercise:
  • The driver needs to determine a new speed after realizing he is 15 minutes behind his usual pace at the 120-mile mark.

  • First, identify known values: the normal speed (55 mph), total distance (440 miles), and distance covered (120 miles).

  • Calculate the remaining distance (440 miles - 120 miles = 320 miles).

  • The usual total travel time is 8 hours, and subtracting the 2.43 hours already used gives 5.57 hours left.

  • To find the speed needed to complete the trip on time, divide the remaining distance by the remaining time, i.e., 320 miles by 5.57 hours (which results in approximately 57.45 miles per hour).
Each step is a small problem that adds up to the full solution. Properly organizing and analyzing data means you can effectively solve complex physics problems by focusing on smaller, critical parts at a time.

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Most popular questions from this chapter

A driver has a reaction time of \(0.50 \mathrm{s}\), and the maximum deceleration of her car is \(6.0 \mathrm{m} / \mathrm{s}^{2}\). She is driving at \(20 \mathrm{m} / \mathrm{s}\) when suddenly she sees an obstacle in the road \(50 \mathrm{m}\) in front of her. Can she stop the car in time to avoid a collision?

If Chameleons can rapidly project their very long tongues to catch nearby insects. The tongue of the tiny Rosette-nosed chameleon has the highest acceleration of a body part of any amniote (reptile, bird, or mammal) ever measured. In a somewhat simplified model of its tongue motion, the tongue, starting from rest, first undergoes a constant-acceleration phase with an astounding magnitude of \(2500 \mathrm{m} / \mathrm{s}^{2} .\) This acceleration brings the tongue up to a final speed of \(5.0 \mathrm{m} / \mathrm{s}\). It continues at this speed for \(22 \mathrm{ms}\) until it hits its target. a. How long does the acceleration phase last? b. What is the total distance traveled by the chameleon's tongue?

Steelhead trout migrate upriver to spawn. Occasionally they need to leap up small waterfalls to continue their journey. Fortunately, steelhead are remarkable jumpers, capable of leaving the water at a speed of \(8.0 \mathrm{m} / \mathrm{s}\). a. What is the maximum height that a steelhead can jump? b. Leaving the water vertically at \(8.0 \mathrm{m} / \mathrm{s},\) a steelhead lands on the top of a waterfall \(1.8 \mathrm{m}\) high. How long is it in the air?

A car is traveling at a steady \(80 \mathrm{km} / \mathrm{h}\) in a \(50 \mathrm{km} / \mathrm{h}\) zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady \(8.0 \mathrm{m} / \mathrm{s}^{2}\) a. How much time elapses before the motorcycle is moving as fast as the car? b. How far is the motorcycle from the car when it reaches this speed?

In springboard diving, the diver strides out to the end of the board, takes a jump onto its end, and uses the resultant spring-like nature of the board to help propel him into the air. Assume that the diver's motion is essentially vertical. He leaves the board, which is \(3.0 \mathrm{m}\) above the water, with a speed of \(6.3 \mathrm{m} / \mathrm{s}\) a. How long is the diver in the air, from the moment he leaves the board until he reaches the water? b. What is the speed of the diver when he reaches the water?
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