Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

Problem 13b

Chapter 2, Problem 13b

How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

Verified step by step guidance

Identify the given information: The car's final velocity is 60 mph. Convert this velocity to SI units (meters per second) using the conversion factor: 1 mile = 1609.34 meters and 1 hour = 3600 seconds. The formula for conversion is:

v = 60 \times \frac{1609.34}{3600}

Determine the acceleration of the car if it is not explicitly given. If the acceleration is provided, note it down. If not, assume a constant acceleration and denote it as

a

Use the kinematic equation to find the distance traveled:

v f^{2} = v i^{2} + 2 a d

, where

v i_{i}

is the initial velocity (assume 0 if the car starts from rest),

v f_{f}

is the final velocity,

a

is the acceleration, and

d

is the distance traveled.

Rearrange the equation to solve for

d

d = \frac{v^{f_{2}} - v^{i_{2}}}{2 a}

. Substitute the known values for

v f_{f}

v i_{i}

, and

a

to calculate

d

in meters.

Convert the distance from meters to feet using the conversion factor: 1 meter = 3.28084 feet. The formula is:

d (ft) = d (m) \times 3.28084

. Provide the final distance in both meters and feet.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Speed and Velocity

Speed is a scalar quantity that measures how fast an object is moving, defined as the distance traveled per unit of time. In this case, the car's speed is given as 60 mph (miles per hour), which can be converted to SI units (meters per second) for consistency in calculations. Understanding speed is crucial for determining how far the car travels over a specific time interval.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. For this question, it involves converting miles to meters and hours to seconds to express the car's speed in SI units. Additionally, converting the final distance from meters to feet is necessary to provide the answer in both requested units, highlighting the importance of dimensional analysis in physics.

Distance Calculation

Distance is calculated using the formula: distance = speed × time. To find out how far the car has traveled at 60 mph, one must specify the time duration for which the car has been traveling. This relationship is fundamental in kinematics, allowing us to determine the total distance covered based on the speed and time of travel.

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