Ch. 01 - Introduction, Measurement, Estimating

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 01 - Introduction, Measurement, Estimating

문제 55b

1장, 문제 55b

The speed v of an object is given by the equation v = At³ ― Bt, where t refers to time. What are the SI units for the constants A and B?

검증된 단계별 안내

Step 1: Start by analyzing the given equation:

v = A t^{3} - B t

. Here,

v

represents speed, which has SI units of meters per second (m/s), and

t

represents time, which has SI units of seconds (s).

Step 2: To determine the SI units of

A

, focus on the term

A t^{3}

. The units of this term must match the units of speed, which are m/s. Since

t^{3}

has units of

s^{3}

, the units of

A

must be m/s⁴ to ensure the product has units of m/s.

Step 3: Next, determine the SI units of

B

. Focus on the term

B t

. The units of this term must also match the units of speed, which are m/s. Since

t

has units of seconds (s), the units of

B

must be m/s² to ensure the product has units of m/s.

Step 4: Summarize the results. The SI units of

A

are m/s⁴, and the SI units of

B

are m/s². These units ensure that the terms in the equation are dimensionally consistent.

Step 5: Verify the dimensional consistency of the equation by substituting the derived units for

A

and

B

. Confirm that both terms on the right-hand side of the equation have units of m/s, matching the units of

v

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Speed

Speed is a measure of how quickly an object moves, defined as the distance traveled per unit of time. In physics, speed is often expressed in meters per second (m/s) in the International System of Units (SI). Understanding the relationship between speed, time, and the variables involved in motion is crucial for analyzing equations that describe motion.

Dimensional Analysis

Dimensional analysis is a method used in physics to convert units and check the consistency of equations. It involves examining the dimensions (such as length, time, mass) of physical quantities to derive the units of constants or variables. This technique is essential for determining the SI units of constants A and B in the given equation.

Constants in Equations of Motion

In equations of motion, constants like A and B represent specific coefficients that influence the behavior of the system. The units of these constants depend on the terms they are associated with in the equation. For example, if A is multiplied by time cubed (t³), its units must balance out to ensure the overall equation maintains consistent units for speed.